There's plenty of threads about competence and working on your own boiler and system, so I won't go into it here.
Without making up statistics on the spot, there is a probability/percentage value, relating to both successful, safe and problem-free diy (or unregistered) work and that which goes on to have catastrophic consequences (and a scale between).
Fortunately, the latter is a much smaller percentage but playing those odds is a risky business as one will not know, until after the fact, into which category they have fallen.
Being "competent" is about having the knowledge, skills, equipment AND backup of a registration scheme in order to leave the equipment you have worked on, in a safe operating condition.
G3 registered covers work on unvented DHW systems where there is a risk of injury and damage due to the uncontrolled release of extremely hot water under pressure and potential explosions. G3 means you have been assessed for competence to work on such systems.