I'm fairly sure this is a straw man argument.
There are a variety of logical fallicies involved in this argument, but no--no, it isn't.
What it really comes down to is how you want to read the phrase "the power's other effects". You can treat damage of type fire and cold as either one effect or two. If you treat it as one then of course immunity protects you from all the damage. If you treat it as two then it does not. Treating it as two effects makes it work quite nicely when it comes to resistances.
...except that that's wrong. The rules are really clear on what's one effect and what's two -- and "25 fire and cold damage" is one thing, one set of damage, and one effect--just one with two keywords.
Immunity is -supposed- to be powerful (though not as powerful as it was when the game was first released).
Lets turn the argument around for a moment:
Compendium said:
Baleful Gaze of the Basilisk
You cast a toxic glance at your foe, leaving it paralyzed with fear.
Daily
Arcane,
Fear,
Implement,
Poison
Standard Action Ranged 10
Target: One creature
Attack: Charisma vs. Fortitude
Hit: The target is stunned and takes ongoing 10 poison damage (save ends both).
Miss: Ongoing 10 poison damage (save ends).
Dragon Magic: When the target saves against the ongoing poison damage, you slide the target a number of squares equal to your Strength modifier.
First published in Player's Handbook 2.
Immunity to poison and immuity to fear both grant immunity to a power's "other effects" (unlike straight damage types).
So, what happens when you use the Baleful Gaze of the Basilisk against a target that's immune to fear?
What about against one that's immune to poison?
My answers, of course, is that the target that's immune to fear taks the ongoing poison, but not the slide or the stun.
A target that's immune to poison is immune to all the effects of the power, as while they're fear effects, they're -also- poison effects and the target is immune to those.
Now, a real GM would probably (correctly) interpret the intent of the power that the slide is a poison effect (mabye) and that the stun is a fear effect. But lets just look at RAW interpretation, not rule-by-intent here. (a similar example is Prismatic Spray--it's easy to figure out which of the three effects are -intended- to be tied to each keyword--but one cannot do so (for the stun effect) without flavor-based interpretation)
Similarly, you're hit with 25 ongoing poison and fear damage. Would Plaguefire body help you?
Compendium said:
Plaguefire Body
You feel your bones burning with an inner fire, and those around you see the faint outline of your skeleton glowing through your skin.
Encounter Arcane
Free Action Personal
Effect: End one poison, disease, charm, or fear effect that currently affects you.
First published in Forgotten Realms Player's Guide.
Basically, it seems like the anti-immunity people in the thread are trying to treat immunity as resistance(infinity). But there's no support for that in the rules text, and you can't get there without more or less making up a rule (either immuity=infinite resistance or the [worse] "damage with multiple types is multiple effects" misrule).