It is difficult being a dog in a human dominated household. Humans say "No, that wouldn't be good for you."
Sure. They say it, but we are all animals. If it good for the human - it is good for the dog. And, more importantly, if it is bad for human, Henry is willing to sacrifice himself for the health of his human.
Yes, he is just that dedicated to Sue's health. Henry's miserable doggie sounds are pathetic when that carmel dulce de leche is disappearing into Sue. Translation is, "No, no. Dear Human, don't do that to yourself. Let me save you!"
....and proving his commitment - the remnants were rescued from the trash, just in case his Human was going to re-establish ownership and clean out the last bits. That is dedication.