> in connection with our provision of the Service.
This is pretty much boilerplate legalese that's generally intended to mean "you can't upload a file to your public folder, then sue us for copyright infringement because that file is in a public folder".
Lawyers seem like to cover their clients' asses as much as possible, but for a service like this that's designed for privacy-conscious people it'd do them well to step back and think about how the license comes across to privacy-conscious laypeople.
From what I've seen of Keybase, from back when they were just an alternative to the PGP Web of Trust to now, I don't think they're genuinely planning anything nefarious (but they'd still do well to have a ToS that reflects that).