Upvoting you to help prevent your comment from reaching oblivion - I don't agree with you, but I think what you said is a common belief.
The thing is, it's a vastly different kind of pressure. When I am coding as part of a job - by myself or with others - there is no inner monologue in the corner of my brain doing something like this:
"Could do that or... no damn, that's O(n^2), damn I'm taking too long that one looks bored, if I instead put those keys in a hash... no, I'm sure there's a better way, running out of time though, is he looking at his phone now? Okay, what was the profile of merge sort again? ... oh, shit! She felt like she had to offer me a guiding hint, I'm doing it wrong!"
And it never stops going. It picks apart every choice I make, and by five minutes into the interview I come across as a sub-articulate mess.
In no other high-pressure situation does this happen to me. Hell, this past summer I actually spoke at a conference and I didn't have the kind of trouble I do in an interview.
Whiteboarding, paired coding, participating in architecture design - these things come easily. In the context of an interview, though, it goes out the window.