I can't believe the Hansens were given all available info on the Borg while Picard, a starfleet captain in charge of the Federation flagship, was left in the dark. It just doesn't add up.
It's possible they stumbled across a small amount of leaked information and used it begin their search for the Borg. The Hansens were clearly bright people, albeit somewhat misguided.
And keep in mind that although Picard was important in the context of The Next Generation
series, he was no more important than any other captain in Starfleet in-universe. Why would Starfleet have any reason to share with him classified data (assuming it was
classified) about a species he'd never seen before?