No, YOU lay down and keep the bike UP. Well, you hope, anyway.
I'm not referring to a countersteer OUT of a corner to, well, counter in that case a rear tire that is itself sliding out of a turn on acceleration.
It's setting up for a turn..the initial front wheel movement is WITH the turn, not COUNTER to the turn.
On a streetbike, the initial movement IS counter. That's what drops the bike into the turn. But, you likely have traction on that streetbike front tire, too. In the dirt on a sharp 90º I can see a countersteer action putting you well into the weeds.