Exactly what was he doing/how was he "training" when he got injured? If he jumped right into deep bodyweight squats or high volume stuff, then sure there's a chance he aggravated something.
So he was very athletic and in great shape, and now he's obese. Did an injury end his athletic training or was it just a lifestyle change, or something else?
How tall is he? It's a small point, but if he's 5'6" or 6'2", it gives a little different picture of the situation. Also, how old is he and how long ago was he in great shape? I'm picturing like a 40-year old guy saying what great shape he was in during his college baseball career 20-something years ago. If he's been out of shape for way longer than he was in shape, it might not have much carryover other than trying to rekindle that attitude for motivation.
I think you might be over-investing in the tendon/ligament thing, unless there's a pre-existing situation I didn't see mentioned yet. Obviously it's worth repeating that the dude should get a basic doctor's check-up, first and foremost.
I agree with what's been said, you can get a running start (pun intended) by cleaning up his diet and doing some consistent walking. Yes, strength training/bodyweight training will be a benefit, but diet and cardio are going to be essential anyway, so the sooner those happen, the better.
You can always regress a bodyweight squat by using something to help stand up (a pair of chairs to push off of, or a partner or anchored rope to help pull up). That would essentially "reduce the resistance" and make the exercise easy enough to do more reps until strength and conditioning is built. But yeah, shotgunning guesses as to what's going on with his knee isn't the way to fix things.