I think F-Droid is a great way to discover apps, but I'm not sure I would trust a binary downloaded from its repository the same I trust a binary downloaded from the app's official website or repository. I also remember a few apps clearly stating the F-Droid repo was a few versions behind and the "right" way was to install from their page.

Anyway, this might all become moot very soon if Google prevents us from installing anything from 3rd-party sources.