If it's limited, then it can be a good thing, for streamlining and have some solid common ground. The problem is when you have to look up multiple places or remember multiple rules. Looking up the spell every time it's cast or looking up multiple rules, what is worse?
The former, because the latter
doesn't happen.
I have literally never been in a group where everyone owns the game book. With 4e though, I noticed nearly everyone uses the Character Builder, so at least they've all got the stuff on their screen. Still, they have all read the PH and know the jargon.
With Pathfinder, that's just not going to happen. To me, making people look things up is an actual time cost; you can have four or five players all wanting to look up the one Pathfinder book there, or maybe just checking things on the SRD, slowing us all down. Fortunately, this doesn't happen much in Pathfinder. Even if players have to look up their spells, they don't need to look up the jargon too. (Well, not too much, and not for basic stuff like actions.)
The second doesn't happen though. People aren't going to look up jargon in play. I think in this case it came up because it's a new rule, causing memory interference with a slightly older one. By the time D&DN actually comes out, this won't be an issue, once the player has looked up the actions and combat section.
Here's an example of how a lack of jargon (so different rules per rule) can hurt the game.
The scenario involves the PCs walking through a dungeon. They know there's a good chance they could be attacked at any moment.
They peek through a keyhole, but there's no light on that side. They quietly pick the lock, but when they open the door there's a bunch of undead (who were silent to that point) looking right at them. Neither side checks for surprise, just roll initiative and either fight or flee.
The group fights. The cleric says he'll turn undead.
3.x: The table groans. The cleric player needs to look up how to Turn Undead in the PH. He asks the DM how many Hit Dice they have. The DM hems and haws, because he's not sure he wants to give out that number. Meanwhile the cleric says he'll just roll, but he doesn't know how many d20s and d6s he's supposed to roll, so he starts fumbling with the dice...
Pathfinder: The player already knows the AoE of Channel Positive Energy. It's standardized. The other details (save DC, damage dice, and number of times per day) are written in short form on his character sheet. He announces the save DC and rolls the d6s of damage. That's it! Standardized jargon really speeds up play, and makes it possible to include relevant details on your character sheet.
Similarly, I can write these details for Fireball on my sheet, assuming I'm very new to the game: 1d6 fire damage per level (max 10d6), spread 40 feet, range Long (since memorizing what "long" means takes no real effort), save DC [listed] for half. That's it. No need to look up the rules. That's why I like jargon.
This is why I made the Barbarian example (but the critique, once again, is not about the resulting limitation on Rage, I don't care about that): because it's a kind of cross-interacting case between three parts of the rules, (1) the definition of reactions, (2) the combat action "Ready" and (3) a class special feature "Rage". The (2) and (3) are apparently disconnected since there's nothing in Ready saying you can't do it during a Rage, and nothing in Rage saying you can't Ready an action, but (1) links them together. I can totally picture my gaming group playing many sessions before realizing the incompatibility between Rage and Ready. And this is just an example of one linking keyword, but the more jargon, the more intricated cases can appear in the game without even the designers noticing.
I can't see your group having a problem with that. The rule is easy to remember.
Player: My raging barbarian wants to ready an action to [something]
DM: You can't take reactions while raging.
Player: Oh.
Even if they get it "wrong", they'll probably be consistent (most likely, by readying actions while raging, because they'll forget that readying an action takes a reaction*; this is hardly game-shattering), which I still think is better than expecting the DM to judge every corner case, and then remember all their judgements so they can remain consistent with them.
*I don't think readying an action takes a reaction even makes sense, which is sure going to make the rule a bit harder to memorize. WotC probably made the change because lots of groups hate shuffling initiative orders.