Question regarding ending

I pretty much figured it was just his appearance, that's how I knew it wasn't him. Even after the passage of 32 years, certain physical traits will remain constant.

There's no "I" in team, but there is an "m" and an "e."

Introducing the possibility of ambiguity is interesting.

Vogel had told the man in 414. When Rachel caught up with the real Vogel he said he wouldn't tell any more stories to the guy in 414.

It's my RIGHT to offend you!!!

On the OP's question regarding the man in the room, I agree that what exactly happened was ambiguous. In this, perhaps as not in other aspects of the film, heh, we see a mix of factors playing out very quickly. As happens now and then in real life, interestingly enough.

The film makes clear that despite her journeying all that distance, Rachel was not sure what she was going to do when she got there. On one hand she wanted to get there before the reporter, and her taking out the injection indicates she was at least preparing to go ahead and kill the man. But it ALSO is quite clear that she was considering David's argument of coming clean, and telling the truth.

I think what happened is her actually being in the room was something that she thought would indicate to her what she should do, and the brief sight of the man, even from a three quarter side rear view, was not enough to give her the impetus to kill him. My own feeling at the moment was doubt it was Vogel. Then when he talked she heard none of Vogel in what what was said. She at that point, having failed to find in her reaction to his presence, and the doubt it was him, enough motivation to kill him, instead pursued the course David suggested, and wrote out the note to the reporter. (I think a small factor was also that Rachel took some satisfaction in calling Stefan and telling him he was wrong, it was not Vogel, but that was a small factor.)

Then, when she sees Vogel, however briefly she nonetheless recognizes him instantly, thirty two years later beside the point, it his him, AND he tries to run away.

At that point Rachel's instinct to track him kicks in, but it's more than that. She remembers his saying that Jews don't know how to kill, remembers Vogel killing many, his taunts come back to her, and on top of that her desire not to let him escape, again, kick in as well.

At a minimum she must chase him, and then encounters him. Even then we are not sure what she will do. She has already left the note in room 414. The truth will come out. What now?

In the back and forth of her now elderly and in some respects both pathetic and still deadly struggle, we realize ambiguity is still present, but Rachel is reacting as much as acting. Vogel is trying to kill her! Is she going to be the victim, like all those Vogel referred to back in the Holocaust?

No.

In total, a rather interesting ending. Is it too much in service of being cathartic to the audience? Perhaps - we get to have Rachel all of telling the truth, risking victimhood (and in fact being injured, again, by Vogel), and nonetheless killing him, as he not only deserved, but also initiated himself in attacking her. Morality is well served, all in all.

But perhaps it is a bit too neat. Well, at least it tied up the loose ends, which is part of good filmmaking.

I suppose in fairness it is not implausible that Vogel over the course of many years might have let slip his story to one of the other patients, and that the patient could have done what he did. So that I don't criticize, either. It served the plot development quite well to have Vogel be glimpsed by Rachel as she left 414, but this is filmmaking, and however unlikely it is that it would have happened like that in real life, it is what happened in this film. I did not feel like it was too challenging to my suspension of disbelief.