Daver, that's a silly statement.
Can't go off-road on a BMX?!? What? They were FIRST designed for off-road!
I own a Norco Speed Metal Pro - a 20 inch race BMX. I used to race BMX with it. I do dirt jumps with it. I've ridden most of Grizzly's Glory with it, including the North Shore sections and ladder drops. I've done the Oaks trail in the Blue Mountains on it. I've ridden several of the trails at Oxford Falls on it. Admittedly, the trail riding was done out of necessity (normal MTB was stolen), but I think it can handle off-road nicely, thank you very much.
I think the best benefit of a BMX over a MTB is that it's a very simple, tough little tank of a bike that you can huck around, and ditch/crash at will, without worrying about breaking, scratching, damaging expensive parts.
Plus, the lower center of gravity for the bike makes it easier to throw around in the air.
And they're usually MUCH cheaper than a comparable quality MTB.
Just don't think you can do a lot of hill-climbing with one. That's pretty evil.