Steve Nash Beer Video -- NOT STAGED ... Says Keystone Light

If you thought that crazy video of Steve Nash getting a road beer on an L.A. Freeway was too good to be true ... you were DEAD WRONG ... so says Keystone Light.

The footage is pretty insane ... an SUV of pumped up Lakers fans spot Nash in a yellow cab ... pull up next to the car ... pass the guy a Keystone Light ... and Nash accepts. The fans go wild.

Nash shot the video on his own cell phone ... which led many to believe it was all a premeditated viral video stunt to promote the beer.

But the honchos at Keystone insist it was as REAL as it gets ... telling TMZ, "While we can take credit for the 'Always Smooth' taste of Keystone Light, we had nothing to do with this video."