No, not really.
I think people who have a weakness are most likely to attack, without evidence, things that expose that weakness as unfair. People in this thread are going so as to call the interview technique of whiteboarding a problem “practically inhumane”.
You are right that I think inability to talk thru ones train of thought on a new problem to them to be a signal of inability. I think whiteboarding exposes this kind of weakness. I also think it has many causes: extreme stress reaction, bad social skills, lack of domain knowledge, bad communication skills, and plain old stupidity.
So to read that “whiteboarding” should be disallowed from interviewing, because it is so much more high stress than every other part of the process, despite those parts also having equal importance in the overall stakes, really needs some elucidation. I accept anecdotes from workers who claim they are only low performers in the interview because of stress or anxiety, but I strongly doubt unmitigated social anxiety presents as a detriment to ones apparent job performance in interviews but not jobs at a high enough rate to give any credence to these claims without some sort of data driven backing.
The only point I am trying to make is that yes, interviews are very different than the other scenarios that you mentioned.
Here's one reason: in an whiteboard problem solving session, the other person has explictly prepared something that they know more about than you. On top of that, you are both aware of this fact. This almost never happens in a normal work-collaboration. A collabaration happens because both parties have something to offer. If not, they'd be explaining to you, and not the other way around.