Is he telling me the truth?
yes
That all depends on how you interpret the regulations.
3. - (1) No person shall carry out any work in relation to a gas fitting or gas storage vessel unless he is competent to do so.
"gas fittings" means gas pipework, valves (other than emergency controls), regulators and meters, and fittings, apparatus and appliances designed for use by consumers of gas for heating, lighting, cooking or other purposes for which gas can be used.
"gas appliance" means an appliance designed for use by a consumer of gas for heating, lighting, cooking or other purposes for which gas can be used ...
If a person does work on a gas fitting
for money, he has to be CORGI registered. But, as the definitions above show, a gas appliance is a gas fitting. So it could easily be argued that the complete boiler is an "appliance" and therefore comes under the definition of a gas fitting and will need a CORGI person.
The regulations make no distinction between the gas side and the water side of the boiler; it is all part of the gas "appliance" and consequently a "gas fitting".