TV Fixings - 40" LED fitted to drywall using one metal stud and snaptoggles is it safe?
I must say that the "carpenter" son seems to be a bit of a non-professional if the description you gave of the installation is correct. Mounting a cantilever arm as described seems to me like it asking for trouble. Even with a smaller sized TV the cantilever arm, when extended, will put a rather large pull out force on the fasteners in the drywall. 

To avoid any unfortunate mishap I really suggest getting that short piece of board removed. It should be replaced with a sturdy piece of 0.75 inch thick plywood that spans at least two studs and has a height of at least two feet so that fasteners into the studs can be spaced a good distance apart near the top and bottom of the plywood. Then remount the cantilever arm plate to the plywood. That should give a very reasonable and secure mount for the TV.

The plywood piece can be sanded and painted up nice before attaching it to the wall. If the color matches to the wall it would blend in well and not appear to be out of place behind the TV.