Well, obviously, you can keep your false-positive rate low by requiring absolute consensus. If you require fourteen different people to agree on every hire, then you're not likely to hire any bad people....you're also not likely to hire anyone at all.

Your second argument is more reasonable: if you stick to strict majority-rule voting, it's true that you're less likely to get a false-negative result with a larger number of voters. (You'll also increase the number of false-positive results). Problem is, nobody actually does it that way. Most hiring managers are trying to keep the false-positive rate low, and tending toward consensus. Thus, random false-negatives have quite a bit of impact -- one or two "no-hire" votes are enough to torpedo a candidate at places like Amazon, Microsoft and Google.

Clearly, when you do enough interviews, you start to expect "no-hire" votes, just due to chance. You can claim that this is good for the company, but like I said before...these companies do a lot of complaining that they can't find "qualified" applicants. Perhaps if they re-thought screening processes that involved dozens of interviews, they might find that the qualified applicants were there all along.