From observations of myself, and my dogs.
Raw egg white might be not as easily digestible as denatured one (inactivated avidin in this case). When I eat whole egg in raw state I'm fine, but when I eat just raw egg white alone I might get diarrhea on occasions, so I don't do it anymore (just raw yolks if I have taste for them).
Same for my dogs, whole raw egg usually do the job, but I've noticed that if they have a choice, they will go for raw egg yolk instead of whole raw egg. They must sense something bad in raw egg whites, and most likely it is avidin which is there to scare of predators (by creating digestion problems). One important thing, I'm talking only about dogs on a 100% raw diet, from the birth, or at least one year into the raw diet.