As I see it, there's a number of different issues here. I don't think these are things everyone will ever agree upon, but I thought I'd drop my two crowns in.
The first issue is the Concordian himself. He's a dwarf who possesses a power that is unavailable to PCs. He's not a mind flayer, or a rakshasa, or something bizarre. How is it that he can have this cool power that a dwarf PC can't?
The second is the power itself... both the Concordian's specific ability, and dominate itself. Should ANYTHING be able to have this level of power?
On the first point: If you're going to allow dominate in the game, I have no problem with the Concordian having it while a PC - even a psion - doesn't have access to it. A few things to consider:
1. The Aurum is a secret society dedicated to dominating others. Eberron is a setting in which magic has been adapted to accomplish the needs of society. Ilithids, vampires, Quori - all of these are creatures that dominate others through innate supernatural power. The Concordian represents the industrial use of magic: a society dedicated to coercion that has developed a powerful tool for accomplishing that goal.
2. Great - they've developed this tool. So why can't YOUR dwarf do it? Others have already suggested a lot of good reasons. First, let's look at all the things your PCs can do that he can't. Your psion can't do it - but what about the huge mass of things your psion can do that he can't? At seventh level, the Concordian only has four powers, compared to the nine powers your PC has. He's a dwarf, so he could live a long time. The way I look at it, he's probably spent seventy years perfecting this skill... honing it with such intensity that he's given up the versatility that your psion has. So could he teach this skill to your psion? Sure! it's just going to take you seventy years to get the hang of it, and in the process you're going to lose your dailies, an encounter, and two utilities because of the intent focus you'll be putting into it.
That's just one approach. A few others:
* The power is similar to the Slayer's Puppet's power of the Dreaming Dark assassin - ranged instead of melee, but the Quori power is save ends instead of one round duration. If you don't like the idea of a dwarf having it... then say that he's not simply a dwarf, he's a Quori mind seed. You know there's some in the Aurum. Or perhaps he's a fiend of the Lords of Dust in dwarf form.
* If you want him to stay a dwarf, perhaps the Concordian only has the power because of a pact he made with an Overlord of the First Age. You can have it too, if you're willing to become an instrument of a demon lord, just waiting for the day when he takes over your body (at which point, you're an NPC... which is one reason only NPCs have the power!)
* Eberron's never had a problem with the idea that certain magic can only be performed by certain bloodlines... IE, dragonmarks. Nowhere in this piece does it say that all members of the Platinum Concord have this power. So, this could very well be a form of blood magic perfected by a particular dwarven family. Your character could learn the power too... if you're a member of that same bloodline. Otherwise, you might be able to learn it... but it would take you a few centuries to develop a version that works for your bloodline, same as it took them to develop it.
* It's all about perspective on the world. D&D generally works on the assumption that PCs, if not heroes, are at least noble on SOME level. It could be that mastering this spell requires an utterly sociopathic mindset that lets you see beings around you as nothing more than tools - that you have to be completely lacking in empathy in order to enforce your will over another. This won't work if your PCs truly are this sort of person - but I have to say, if they are, yecch.
But in general... Eberron's always taken the approach that PCs and NPCs work in different ways. The Eldritch Machine is an example of saying "do whatever it is that makes the story work the way you want it to." The idea that an evil mastermind has some evil spell or weapon that his heroic opponent can't use or develop on his own - despite being just as intelligent as the villain - is a well-established pulp trope.
I didn't design the Concordian, but I'm guessing the logic of the designer was something like this: An elite monster counts as two monsters. The Concordian accomplishes this by BEING two monsters - one of whom is one of the PCs. He can't ever control more than one and has to continually work to maintain control. The logic is flawed because the PCs lose an asset in the process, but the Concordian has to actually make the attack and hit with it. The power itself is Ranged 5, which first means that he's screwed if the party stays out of range, and additionally that he draws melee attacks of opportunity when he uses it. In addition, while it's a minor action, I've seen lots of groups that can keep a bad guy dazed for a good long time. It's a scary, powerful ability - but by comparison, the Dreaming Dark Assassin or Belashyrra could end up dominating an entire party.
As for dominate itself... I really, really hate excessive use of dominate. I hate it when one PC ends up having to sit on the sidelines. However, I feel that there is a place for it, just as you had dominate, suggestion, and any number of other mind-influencing effects in third edition. If I were to use it, I'd do the following things.
* Severely limit the number of enemies with dominate. I was in a campaign where we were getting dominated literally every other adventure, and it sucked hard. There was no flavor to it - just "Again with the dominate." If the Concordian is The Enemy With Dominate, and we only see him every four adventures or so, that's fine with me - and I'm going to really hate that guy.
* Play up the ability when dealing with the character, preferably in noncombat situations. So, the first time we meet the Concordian, he's actually hiring us to do a job (though he's going to double-cross us later). Let's see him humiliate the barmaid or cause another employ who failed him to cut his own throat. Emphasize that this is a scary and extremely remarkable power that he possesses, that it is the REASON he has become this amazingly wealthy and influential person. He's not just dominating you; domination is his defining characteristic, something he has honed and perfected, not just a trick any wizard could learn. Look at the Purple Man in Marvel Comics, how he uses the power casually and cruelly as well as when fighting superheroes. Personally, I'd be inclined to say that on normal NPCs the power last even longer (though still only one person at a time) - the fact that it only lasts a round on a PC reflects their strength of character and how difficult it is to maintain control.
* If your PCs are decent roleplayers, let them keep complete control of their characters when dominated. Make it a roleplaying challenge. Don't say "Joe uses Tide of Iron on Bob." Say "Joe, the Concordian is like a father figure to you. He's saved your life. He's the only one who can save your sister from (fill in plot hook). All of the other PCs have betrayed you. Now Bob is going to kill the Concordian. What do you do?" Obviously they are still limited by the conditions of dominate, so they can't burn dailies and such - but let THEM play it. Let the fighter say "Not so easy without me to hide behind, huh, shrimp?" to the wizard. Don't be mindless zombies - let out repressed frustrations. So then, when the fight is over, you have to deal with the things you've all revealed.
Dominate still sucks... I guess I'm just saying that in small doses you may be able to find ways to make it suck less, especially if you really play up the flavor of the character and just how remarkable and scary the power is.