It does...the teleport ability specifically states: Being immobilized or restrained doesn’t prevent a target from teleporting. If a target teleports away from a [BOLD]physical restraint[/BOLD], a monster’s grasp, or some other immobilizing effect that is located in a specific space, the target is no longer immobilized or restrained.
Right - which doesn't help a person who is manacled, for example. They'd teleport to a different space, and still be manacled. Assuming a definition of manacles that matches the usual ones - ie, heavy duty handcuffs chained together. Any more than they'd teleport away and no longer take ongoing damage from a swarm because they left behind the little creatures biting them, or ongoing acid and fire cause they left behind those effects, or no longer diseased because they left behind harmful viruses and bacteria, etc.
Being manacled, mind you, wouldn't immobilize someone. You can still move around while manacled.
As a compromise, I think it would be fair interpret the rule to be that if the movement uses a mode of movement that you do not possess
I think any DM that rules that you can't use Close Quarters on a dragon to hang on while it flies around is doing a disservice to their players. That's the epitome of the kind of effect that it's there for.
Allowing teleport or phasing through a wall, or swarming through a tiny opening, to get out of it is pretty viable. I actually find the phasing and swarming methods work best, because the rogue is taking up space in the movement. You can justify tagging along for a teleport, but the rogue's "space" doesn't fit through the phasing or tiny opening so they might get lose there. Or the creature can't move themselves through, because their movement is constrained by the rogue as well holding onto them. That's one option too. Eh.
Thankfully, I haven't had a player with the power to worry about it, but it's high enough level that you'd expect the teleport option to just come up, and I don't see that ruling against the rogue on it really adds anything to the game.