The meat cornish cross broilers are bred to grow so fast their bones and organs cannot keep up. They are a totally different animal compared to a true pure Cornish. The broiler's hearts fail (complex, here's why:
http://www.merckvetmanual.com/mvm/p...s_of_poultry/ascites_syndrome_in_poultry.html ) and their soft growing skeletons cannot hold up the weight of their massive bodies. By restricting their food in theory you slow the growth rate so that the heart and skeleton can "keep up". A way to restrict their feed is to make them rustle their own food by free ranging- by adding grass and greens and whatever bugs they can catch, gives them far fewer calories than if they had their beaks in the feed trough 24/7 .
The feed I had for my Buckeyes and Dark Cornish was 23% turkey starter and there was meat protein in it as well (pork meal). I don't see any problem myself with leftover cooked buffet meats as long as they weren't marinated in high salt sauces. You don't need to feed a whole lot of meat protein, it should be a part of their diet but not their whole diet. What you want is a proper balance of all nutrients,all essential amino acids, minerals and energy, and without feeding to excess. Water quality and quantity is critical too. This is something that's often neglected, water should be clean, easily available and plentiful all year. Feeding snow to chickens is not a substitute for fresh water.
Pure cornish (and other breeds) are not immune to heart failure either. With large breeds like this, feed management is important. Actually it's important that the different types of chickens get what's proper nutrition for them- feeding light layers too much too quickly causes problems too, but more related to too early egg laying. No easy answers, you have to keep records and find what works best for your breeds and management system.
As with every other thing it seems that excess feed/nutrition causes more problems than underfeeding. You don't want fat chickens of any breed.