I wouldn’t have guessed this either! That button makes me (also) so nervous, that I would actually suggest anyone reading this also do some test cases on a copy or two before pulling trigger on a complex app. Even though I’m confident in my discovery, the thought of others pressing that dang button still makes me uneasy - haha.
Also I was struggling trying to imagine what the wording on that pop-up should be, but you’re absolutely 
right - pressing the sync button should just attempt the sync, clear the error if the sync is successful, and then only pop-up the warning if a problem remains. Yessssss.