As I jest with my partner, you've been watching too many hunting shows on TV.
Seriously, I see more whitetail run for 100 yards with no heart than all other animals I've shot combined. I shot one last year with my 7mm Rem Mag at 85 yards, took off part of his heart and he trotted off 60 yards like nothing happened. It's just the norm with whitetails - they don't know they've been shot until they fall over.
Unless, of course, there's a TV crew filming.