The contamination of meat generally comes from the animal's digestive track, which is why rare red meat is fine - it doesn't get "into" the meat and only sits on the surface, so so long as the outside of the meat is flash fried, the bacteria will be killed no matter how raw the inside is. Chicken is different because the bacteria can get "inside" the meat so it has to be cooked all the way through to be sure that any bacteria is killed.
Also
rare burgers are a no-no because when meat is minced, any external bacteria is minced right along with it. They serve rare burgers in France... it's gross...
.
To go back to dogs though, my dog eats
actual sh*t on a regular basis so, again, I don't think traces of digestive matter on raw meat really compares to that
.