I agree they should have been nicer in their response. Again, I didn't mean to come off as harsh, I just always see these posts like "oh I sent in my secondary and I just realized their LOR requirement, do you think they'll change it for me?" and it just doesn't make sense to me. Sorry if I misunderstood your post-- I thought you had emailed after applying.
I think unfortunately, the admissions process is so competitive that they look for any reason to cut down on the amount of apps they have to review. Particularly for PCOM, which gets so many apps each year. It sucks that they didn't take the time to understand your situation, but I'm sure you'll get in somewhere fantastic! Good luck