Don't be stupid. Animals that are put to sleep don't suffer the fear and pain of drowning. The person putting the animal to sleep doesn't enjoy it and get someone to film it and post it on the internet.
And yes sometimes the person putting the animal to sleep does cry.
If she were to say...put a gun to the puppy's head and fire would you consider that ok? Certainly they don't feel pain, they'd die instantly. And I doubt they'd have any fear either, they don't know what a gun is.