I feel like you missed the part where he said he has to drop weight to meet certain requirements. If his legs are truly 27", and he doesn't feel like he's going to be able to lose adequate bodyfat to meet the requirements, this seems like a reasonable place to start.
Also, I don't know how big your legs are, but I can assure you that running with larger legs is not particularly comfortable. I was a much better runner when my legs were smaller.
I'm surprised anyone's suggesting to keep training your legs with weights. If you're seriously striving to lose 3-5 inches off your thighs, it's going to take forever if you keep squatting. There's no harm in laying off leg work completely for a couple months to reach a particular goal.
Jogging is a good idea, and I would lower your caloric intake. You may not be able to lose a ton of fat, but I would imagine you could comfortably lose at least 20 lbs of fat at the size I think you probably are.