There's no reason to conclude that the Hansen's just randomly happened upon the information about the Borg.
Why not? Are we ruling out the credibility or indeed possibility of Sasquatch hunting in the 24th century? That sounds like an awfully arbitrary limitation on the Star Trek universe.
We the audience know that the Borg are kind of important and very real. The citizens of the 24th century Federation should not have knowledge of either sort. They should retain the right to treat the Borg as a hobby project or a myth of limited interest. And so, really, should Starfleet.