Being the nerdy, mathematical type, I computed the trucker's speed as 65 MPH (road stripes are 40' from center to center, so you can estimate speed by counting the stripes per amount of time). Based on a typical 40' length for the motorhome and that it took 4 seconds to pass (front to back), the motorhome was going approximately 8 mph faster, so 73 MPH.
I've seen comments on the video via different sources and many of them tend to point to speed as a factor. I beg to differ. I suspect that with the same driver under similar conditions at even 55 MPH the same thing probably would have happened. When you lose a front tire on any vehicle, the steering and control changes very drastically very quickly. If you are toodling along with two fingers wrapped around a steering wheel spoke or a wrist hanging over the top of the wheel (guilty), this will likely happen.
There are several good articles on driving through a blow-out, so I won't link any here. The key factor was not to slam on the brakes or yank the steering wheel to try to offset it. It seems counter-intuitive, but most articles mention that your initial reaction should actually be to accelerate briefly before carefully letting the vehicle bleed off speed before pulling over to the shoulder.
There's a slightly better quality version of the video here on YouTube. You can see that the RV driver just briefly taps his brakes right after the swerve starts.
http://youtu.be/lX5EUKYjVfI