An Iron Stomach, Or No?

I have a doctor friend of mine who occasionally tells the story of the time I walked around for three days with a burst appendix.  She tells it to other doctors.  The punchline is, “…and he lived!”
So yeah.  Should be dead right now, but the burst appendix was a window opened for me to look at my rather freakish physiology, which I’ve always taken for granted – but apparently, I have a ridiculously high pain tolerance and an iron stomach that can devour just about anything and not get sick.  In fact, I hate it when I get the flu, because I’m always stuck for hours in that horrific position where the body tells me, Everyone else is firmly in favor of ejecting all the food in your body, except for the stomach.  He is the lone holdout.  Talk to him, sir, we’re all suffering here.
So I’ve been slowly learning that not everyone else does things.  This morning was another, and so I ask:
Occasionally, if I don’t finish a glass of milk at night, and accidentally leave it out, I’ll drink the leftovers the next morning.  Waste not, want not, say I.  It’s a little warm, but tastes fine otherwise – I’m not crazy enough to drink sour milk.
My wife, however, thinks this is just another symptom of my freakish immune system.  If she did that, she’d get ill.  I assure her it doesn’t taste bad, but that’s not the point – it’d still give her food poisoning.  I point out that people on the frontier had to drink warm milk and they didn’t die, and she in return points out that we’re not really living on the plains of Kansas.  Point.
So I ask you folks: could you drink a swallow or two of milk that smells fine that’s been left out overnight?  Would you?  Am I just sufficiently able to shrug off such stuff that I’ve never noted the weaknesses before, or is it something that’s normal (if not, you know, polite) and most people’s systems can handle it?  I’m curious.