...And I've had multiple doctors make me wait an hour+ for appointments that I showed up on time or early for. If I'm only 10-15 minutes late, I certainly expect to still be seen while I'm there. And I always have been.
Life happens. I don't chew out the doctor/receptionist who makes me wait for my appointment that I was on time for, and they accommodate me when I'm running a few minutes late, myself.
Same concept applies at WDW. I've been made to endure long waits for some ADRs, and I've also shown up late to some ADRs (including popular ones like Ohana) and have never been turned away.