#1 There are generally 2 sides to every story. Animal shelters who put dogs in foster care generally aren't 'kill-happy'.
#2 You can fill 100 hours of video clips of dangerous dogs behaving well, especially when it's just the owner and the dog in empty spaces. There is a surprising absence of interactions with other humans and other animals in the video content, not the kind of video I'd expect to see if someone was arguing that a dog wasn't a bite threat.
#3 Triage. 4 million dogs go into shelters annually. 2 million of those are put down annually. Until we can get overall 'put to sleep because there are too many dogs and not enough homes' into the low hundred thousands, I believe we must view every one through the lens of triage. Of the 2 million that are put down, how is Jenny better than any/all of them? The money and effort it takes to save one dog that may or may not be a bite-risk can probably save 10 dogs that have zero bite risk.