Only I wasn't late on my rent. I checked my lease for the amount due per month, and my bank statement for the amount written on the check that they'd cashed June 3rd, and lo and behold, they match!
Now I just need to somehow get in contact with them to work this out.
EDIT: It took some doing to track down the manager this morning -- he wasn't in his office, but he was on-site, and one of the workers pointed me to the apartment he was probably working on. They gave me the wrong number, but I found him.
Turns out it was a computer error that they'd already fixed, but they hadn't sent out retractions because most of the overdue notices were to people who no longer lived in the complex -- I was the only tenant who'd gotten an overdue notice in my own name.
And the delay replacing the fridge was because he's the new manager and hadn't been added to the account that let him make those kinds of purchases yet.
GOD, I was stressing out about it all night, to the point where I had trouble sleeping. ... well, a little trouble. Not as much trouble as if I'd eaten mexican for dinner or anything.