I have seen dogs with E. coli infections at work, in fact, although we use disinfectant to clean all surfaces that are dirtied, we had a small outbreak and had to do a serious cleaning over the entire hospital (wich means, wipe down, wait 30 minutes, wipe down again twice more, then wait 4 hours and wipe down again, ugg). I believe I have also seen a salmonella infection (I think it was a puppy... though I see a LOT of animals...)
I'm not claiming that this is a more of a health threat then anything else, but in both cases the staff were instructed to wash well after handling.
I've seen many posts here that talked about people seeing their dogs pass underwear, socks, tampons, etc, without a problem. I personally know the history of a dog who deteriorated in a matter of days and then died before we could help him, the cause? On necropsy the veterinarian pulled a Tea Towel from his intestines.
Like many people have mentioned in this thread, it is possible to mark almost anything with cause for concern, and we do live in a world that seems to take the littlest threat and turn it into impending doom (I saw a news bit recently about sewing your childs bathrobe tie into his bathrobe because if you do not, it could be deadly).
I just wanted to mention this example to help people put things in perspective a little.
In my own experience, 100's of 1000's of dogs chew sticks, my own dog did so and almost died from an abscess that started from a stick splinter in his throat, now we stay away from sticks. He'll also swallow hard bits of plastic and chunks of what he's chewing sometimes, so no cheapo toys and not tennis balls ; again, many dogs are fine with these items.
Most likely, the result of this discussion could be, if your dog is known for his "sensitive stomach" its likely that his digestive tract is a weak area for him and he should not be fed things like raw meats and eggs, the same should be said for an immunosuppressed individual, very old dogs, or young puppies.
I'm not trying to start any arguments but just popping a bit of my own personal experience into this discussion, again, especially for someone new to dogs, perspective is handy.