Cutting through all the other stuff.
An employee cannot legally work on his own jobs without their own registration. They are classed as Operatives of the company.
Gas Safe rules demand the registration of a fitted heat producing appliance, an Operative obviously cannot do this.
BG absolutely do not allow employees to have their own Reg, and if an existing RGI gains BG employment, he is required as a condition of service to cancel it.
If he is a contractor, then he is free to do as he wishes. But he would then not be a “tame” BG guy. If that is the case then the term is even more condanceding.
To sum up, if he is a BG guy, then he should not be doing it, and your son, without the boiler being properly registered, will have warranty issues.