Agreed, there are likely more shotguns than other guns for a combination of those two reasons (although it should be noted, antique guns can be licensed moderately easily too, I believe. You don't need a license at all if you have them modified so they won't fire. Muzzle loading pistols can be licensed too.) However, overall gun usage in crimes (assuming you don't count people with airsoft pistols pretending they're real, lol) is pretty low. It'd be pretty difficult to hide a shotgun on your person.
Obviously there are people who are against it, as you can find with any new law. I doubt the NRA chose a random selection of people to interview, and then included all of those people in that video. I agree that it's ridiculous about the Olympic pistol shooting (I think it should be able to be done at licensed clubs, as with other forms of firearm), however, she'd still be able to train in Britain, under the British flag, since Northern Ireland allow you to be licensed to own handguns.
