I suspect there are a lot more people who frequently choke on easy coding questions, under the very specific conditions of interview-stress (which is very different from, "the client is unhappy and is also onsite and you'll be in a meeting with them later" stress, and from "production broke" stress, so no, I don't think it's a good proxy for general "grace under fire", as it were, either) than there are actual full-on bullshitters who manage to land software jobs while being truly incapable of doing even the basics of the job.
For one thing, I think such top-tier, extremely-convincing bullshitters would have an easier and less-stressful time applying that skill directly to some other role, since there are some well-paid roles where that kind of thing is exactly what companies want, so it doesn't pass the smell test for me that so very many would be trying to land software jobs—not just ones who exaggerate skill or try to get into the industry while woefully unprepared, but who also are able to fool interviewers at a reasonably-high rate in conversational interviews, yet fail simple coding tests.
That is, I suspect a large majority of "ha! I caught a faker!" anecdotes or anec-data are actually a false-negative on the test from people choking under interview conditions, and that most real fakers would also have been caught in any half-competent conversational interview anyway.
The remainder should be probably be hired regardless, then re-homed to sales when you realize what's going on, since they're evidently top-percentile bullshitters and social chameleons. Joking, of course... kinda. Maybe.