Actually, he can if he has an 07 FFL (manufacturer) and a Class 2 SOT (Special Occupational Taxpayer). The full auto gun then can never be transferred, except to LE or military, or to another FFL/SOT who has a demonstration request letter from a LE agency. It cannot be converted back to semi-auto (once a machine gun, always a machine gun under current US law). If it is not otherwise legally transferred and the FFL gives up his/her license, it has to be destroyed.
1. He must be a licensed manufacturer, and to legally get that license he has to be in business to justify it. So, he may be making it for his own enjoyment, but he's only legally allowed to do so because of his business
2. He can only possess it as long as he's in business because as soon as he's no longer in business, the license goes away and when the license goes away, so does the gun. So he may be making the gun for his own enjoyment, but the gun is never really his
So he's not making the gun for himself because it's never his gun, and the only reason he can make it is because of his business. Most people would say that if you make something that never permanently belongs to you and that you can only posess by virtue of, and during your employement in a certain profession and while you have a particular license then you made it and have it for work and because of work, not really for your "own enjoyment".