"in the sense that their stomach physiology isn't capable of digesting it"
Its a very popular strightdope urban legend discussion topic. You'd die pretty quickly if you couldn't adsorb complete proteins. Astrologically speaking, iron ions from spinach are dramatically different than iron ions from a steak, but your biochemistry won't know the difference.
You can get three interesting effects:
1) Any time you mess with your diet you mess with your gut flora and ... residue. Not to mention the "feel" in your stomach before its all broken down to constituent molecules indistinguishable from plant sources (other than less fiber) So minor tummy ache is theoretically possible. Less fiber intake = less... output the next day, etc.
2) From my M-i-Ls adventures in gallbladder problems, its theoretically possible for vegan types to chug olive oil especially in the form of salad dressing, but to really consume huge quantities of oil/fat all at once you need a greasy triple cheeseburger with bacon. So you can have some bile / gallbladder related fun (whoa I just ate three days worth of oils/greases in one meal, totally freaking out my gallbladder type of reaction). You'll be fine.
3) Psychologically you can get really messed up. Try eating some dog sometime in a foreign country and then focusing on your stomach (assuming you're standard American) is going to be all messed up. Still meat is meat and if they told you it was pork you wouldn't have blinked, but here you are feeling like you're gonna hurl. Its really not as much fun as my description sounds. Think of that soy stuff instead of cows/chicken/fish/pigs/dogs and you'll be just fine as long as you can avoid getting all anxious. Being anxious is never fun, no matter if due to diet or relationships or tiny enclosed spaces or public speaking or whatever.