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I really don't see what the big mystery is. Send the number the school asks for. I suspect the marginal value of additional letters is low. If you haven't convinced them to admit you with 3 letters, is the 4th really going to do the trick? If it was so much better than the other letters, why wasn't it one of the first you chose?
I do think the adcoms want to be fair. They don't want to penalize people who follow instructions relative to those who send additional material. If you are going to send more than the requested number of letters, IMO there should be a good reason -- more than "look, LOTS of people like me" or "well, no one thinks I'm going to win a Nobel Prize, but I can find a lot of people who think I'll pass, so I'll send lots of B+ letters to make up for not having three A letters."
Of course, the flip side is that adcoms want to have as much information as possible when making their decisions. If all four letters really add something unique, then go ahead and send them all. But don't just try to bury them with paperwork or replace quality with quantity.
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