Wow, five days without an answer. Here you go.
I'm assuming you are talking about wrapping meat in foil, or crutching as it is called. The advantage is that when you wrap the meat with a little liquid, you essential steam the meat, a process similar to braising, transferring heat energy more rapidly to the meat. Braising liquid transfers heat 25 times faster than air alone to meat, and liquids wrapped in the foil expand 1600-1700 times when flashed to steam. All that heat energy gets transferred to the cooler meat, consequently the meat cooks faster and the wrapping helps keep the meat moist because all the liquids in the meat are contained in the wrap and not evaporated.
I've never had meat stick to the foil but I always add a liquid, or a very wet veggie (tomatoes, salsa, etc) to my wraps. Don't know what the sticking issue is you had but you could always spray the foil that's going to touch the meat with a veggie oil if it was a concern. I go through cans of that stuff because I always spray my drip pans, or the foil lining, to speed the cleanup once I'm done.