Upvote. You have no way of knowing if that computer is compromised, say with bogus root SSL certificates to allow MitM of ostensibly secure web sites.

What if you store passwords for non-ssl sites in your password manager? I have passwords for some really old mailing lists that don't use SSL and had a big warning that they're completely insecure on the page. I especially don't want to use a shared password if it has a decent chance of being compromised, but if I cared if that account got compromised I wouldn't have set it up.

So basically, you should never use public computers for anything beyond looking at YouTube anonymously?

And searching things that you can't search for at home or on your phone.

The kinds of things that people get put on watchlist for, like where to buy industrial quantities of hydrofluoric acid.