The layer ration is not just about protein. It also contains calcium, vitamins, and other nutrients in proportions to give a BALANCED ration. When you start feeding other things, you upset that balance.
I agree with Cindy that % protein is not all that critical in a backyard flock. The perfectly balanced ration will give you the best efficiency in egg production, but the extra bugs, greens, etc is what makes our eggs special. And if they eat something other than the feed we pay for, our feed costs may come down per egg anyway. I'll give up a few eggs in the name of efficiency to get the better eggs.
The risk I see is that if you give them too much of any one thing, you upset that balance, even if that one thing is something that is "good" for them. And scratch, which can be corn and other grains, is high in energy which can make them fat internally. Fat builds up on their heart, liver and other organs, which can lead to organ failure. Not that it kills them immediately. They may live for years that way, but it is certainly not healthy and the potential for death is there. Fat also builds up in great gobs in the vent area. This can lead to a hen becoming egg bound. When people say to not feed too much scratch, this internal fat is a large part of what they are talking about.