@ossobuco,
Being a more recent observer of doggy behavior, I've noticed some dogs get anxious as part of group when eating. They sometime will meat too fast and suffer a bit of upset afterwards. The habit of eating vomit afterwards is a common dog behavior. To dogs, they don't see the behavior as gross like us picky humans do.
This assumes there isn't already some sort of digestive problem as a result of eating non-doggy food (like human food from table) or some plant irritant from outside. My aged sister was feeding her poodle Cheetos and odd table scraps and her dog was getting irritated digestive tract. Stopping the behavior eliminated the problem.
Also, in the case of my own dog's digestive problems, I changed her diet from no-cereal dog food. I switched her to higher quality ingredients (Blue Buffalo) and problems went away.