In the case of weight lifting, it's usually the mind, not the body, that leads to injury. Crossfit is probably the fastest way to injure yourself, followed by trying to lift more than you should. It's injury prone to make your body do more than it should, you can lift heavy and not do this. Similarly, it's quite easy to stay in the good form zone and still get a good workout. You aren't going to be Ronnie Coleman, but you'll be healthy.

And yeah, I hope no one is claiming that weight lifting trains your aerobic system.