Usually had no problem doing this as well. Only once was the hotel a stickler about it (called some 30 minutes after the cutoff due to a VDB, and they insisted that they wanted to charge me). It was DC of course (you know how people can be there with rules).
Anyhow, got to the hotel the next day at 8:30 a.m. on my rebooked flight, and they try to tell me it's too early to check in. I said absolutely not, I'm paying for last night, so either produce a room, or produce a refund.
They scrambled for a few minutes and were able to produce a room.