The scrum is definitely not good, and is the main source of degenerative spinal injuries. The bulk of other injuries are muscular (sprains, pulls) and bruises. The rules of the game enforce a direction of play that makes head on attacks far less (maybe even none) likely than American football. But it's still a brutal sport with lasting repetitive use injuries - they just don't tend to be head injuries as much.

I think it might be simply because the risk to the person doing the hitting is much greater given they're not covered in pads/helmets. People still get wrecked in rugby, but I think there are less battering-ram style hits.

>Is rugby safer?

The short answer is almost certainly yes but the patterns of injury are different. Rugby also has issues with concussions, although less so than American football. The bigger problem is generally considered to be spinal injuries in scrums.

Unfortunately it's hard to catch much rugby on TV in the US. (I assume there are special packages you can subscribe to but I don't care that much.)

Rugby is occasionally on TV in the US. NBC Sports carries some events. Or, if you want a quick fix, look for a sevens tournament on YouTube (US has a collegiate championship, there's the Olympics, and a few major international). The games are short and fast paced, so easily consumed.