Not true. All of our milkers, bucks, dries and kids are fed a 13% protien year round, and our does milk very well all year round, and everybody is in great shape. Our boer wethers were 50-70 lbs at 3 months of age, and all the doelings, dairy and meat, weren't far behind. None of the goats are fat either.
Ideally, with food, it should be either high protien low energy, or low protien high energy(like barley, oats, and wheat)
If you are worried about the protien, supplement with a good hay.