What the little girl in the video is talking about has nothing to do with assault weapons or high capacity magazines. I don't think many colleges' shooting teams use assault rifles or HCMs in their competition.
But, that really doesn't make all that much difference to how I see the issue. I'm for background checks 100% of the time, yes, even when Bubba sells a hunting rifle to Jethro. It can be handled exactly like when Jethro sells his used truck to Bubba. A title has to be exchanged and the same would be true with a gun. A gun or rifle is someting that ought to be titled like a car. They're dangerous and should require a license to use. Hell, gun shops would jump at the chance to make some $ administering a background check and handling the paperwork just like the DMV does. It ain't that hard. As far as the fee goes, fu*k it, it's just a cost of doing business - big freaking deal.