I called and asked about this because I've been very busy since I finished undergrad so there was a lot of ground to cover in letters.
The admissions lady was, I guess, feeling outlandishly candid that day. She told me that although the school in question claimed to have a strict limit of three letters, the truth was that they just got tired of frantic, overachieving candidates (which, based on a casual survey of today's pre-allopathic posts, describes a fairly large proportion of us) sending 12 bazillion letters "just in case." Apparently the administrative burden that creates was getting to them.
What that means in terms of what you should do I'm not certain, but I can say that, at least in some cases, calling and asking them about it is a good idea. Then again, you might get an answer you don't like, and it's always easier to beg forgiveness than work around denied permission😀 Perhaps you should just launch the battery and send flowers to the secretary later.
I agree that you should not send fluffy LOR's just to make your file thicker, but that, like Neuronix, I had good luck with including a decent spread.