Completely agree. I once had somebody ask me during an interview to write a binary search on the white board. Very tough in that circumstance for me, completely blew it. Interestingly that was 11 years ago, I am now the chief architect and the other fellow has been gone for years. I doubt I could today just stand up and write a binary search from scratch that was worth darn. Even though it is not that tough of a problem.
Programming in my opinion is a reading comprehension skill, solving cute little technical problems won't build large scale maintainable solutions. Even though they are fun to throw around at interviews they don't prove much. :)
First, I never suggested giving every dummy off the street a pass if they blow the technical portion of the interview. You're right: mistakes are acceptable. Given that, you have to base your decision on whether the person is a match for your needs on more than just a coding exercise during an interview.
Second, and more importantly, a coding exercise during an interview is long, long way from working in a startup, or working of pretty much any kind -- unless you've somehow managed to find a way to get paid for solving toy problems. I've done both, and both are hard, but in different ways. To use running analogies, working in a startup (in my experience) is a relay: you have a team, each of you is carrying your own respective bit of the endeavor, but the success or failure proposition is net across the team. In an interview, you're running a sprint, and all eyes are on you, and you alone. One feels completely different from the other, because it is.
Also, half the times (for a sample size of two) I've been asked to do a code exercise during an interview, the interviewer realized halfway through the exercise that he'd misrepresented the specifications of the widget I was supposed to make. The plural of "anecdote" may not be "data", but I've seen and heard, and can conceive of enough problems with the practice of interview coding exercises that I just can't trust them for anything more than exploring how a candidate approaches programming: the way they think.