^^^ i would take him up on his offer but yeah calipers is the best way to gauge this. Figure out your weight and body fat percentage by the pinch/caliper test. simple math after that to find out how many lbs of fat you have lost and the rest is considered muscle gain when you track it over time.
My first measurement said that my body fat is 15%. After 1 cycle of insanity training and 2 km (1.2 miles) swimming almost everyday, now my body fat content is 11%. However my weight remains the same 115 lbs. I assume I gained muscles and lost fat.
I use a scale that gives my body fat percentage. However, I'm guessing that if you weigh yourself consistently and get a good feeling for how much you weigh hydrated, you don't have too many other variables. You're not going to gain bone or tendon. It'll pretty much all be water, muscle or fat.