Several experts have stated that while running
can cause joint damage if done improperly, most people who claim running causes joint damage have previous injuries or arthritis - Neither of which are caused directly by running, but are sure indicators that a person shouldn't be running. That doesn't make running bad for people who don't have those problems. In fact, running may help people who are in danger of developing arthritis later in life.
You're also wrong in that weight lifting burns more calories.
This weight calculator even puts jogging over "vigorous weightlifting" for calories burned.
Other sources drop running a mile at burning about 100 calories for every mile. I found one good article on calories burned lifting weights
here, which puts lifting weights at burning 250 - 450 calories an hour depending on the intensity. If you run about a mile in ten minutes, you'll burn 1000 calories in an hour. That's two to four times the number of calories burned, and a ten-minute mile isn't considered all that fast. You won't look like the Terminator if all you do is run, but there are worse things you could do for your health.
Concerning sub optimal workouts, that last article also mentions this: "... research has indicated that combining cardio with regular weight training burns more fat " - IE Calories - " overall than if you just performed weight training alone, or only cardio." So yes, his workout isn't optimal for burning calories. Just not in the way you're claiming.
Also, BMI isn't
the way determine whether someone is a healthy weight or not. There's a lot more factors than BMI takes into account. Sure, BMI is an indicator of health, but it doesn't tell you how healthy you
are. It ignores heart health, diet, and doesn't differentiate between fat and muscle. Rather than stressing over your BMI, it'd be better to just focus on being healthier in general - Aim to keep your fat levels healthy, exercise, eat well, and you'll be alright. Your exercise and diet shouldn't start and end with making your BMI "ideal".
This article talks a bit about it.
It's pure science - Now with citations.