Yes, sort of.
The feeds that we buy are scientifically formulated to be the most efficient at getting hens to lay, starting with how they are fed from hatch onward. When we let them eat anything other than the formulated feed, that perfect balance is upset. They become less efficient.
However, if they eat only the formulated feeds, your eggs will wind up being no different from the ones you buy in the store. It is the greens, bugs, seeds etc that they eat other than the formulated feed that gives our eggs the character they have. The color and flavor is definitely different. Some would say that our eggs are more nutricious but I'd just say our nutricional values differ. Depends on what they eat.
As far as the efficiency goes, if you have a commercial operation where you have 10,000 laying hens in each of 4 coops or 3 coops of 50,000 meat birds, a difference in efficiency of 1% or 2% is significant and may be the difference in going broke or making a profit. For most of us, a 10% difference in efficiency means maybe one more or less egg a day or maybe we have to feed them a few extra days before we butcher meat birds. Quite a difference.
Your FIL has a valid point. They do need to eat a balanced ration. If you give them too much of one thing it would be like giving a heavy diet of candy to a growing child. They will not develop or function right. For example, if you give them too much corn, they can develop a liver disease. It's the high energy that does it. How we handle this is a personal choice, from limiting them to a small amount of extra to those that let them out every day to eat all the greens, bugs, and seeds they can find.