What might be happening here, is the boilers call for heat input is an electronic input rather than an electrical input. In the old days this would drive something like a relay coil with a fairly low impedance. but if the manufacturers have now re designed it with a new electronic control board, then it could well have a very high input impedance and worse it could trigger from a stray voltage.
Sadly this sort of electronics in boilers is much more common now.
As an experiment try loading the call for heat input with a resistor to neutral or even a low power lamp, just to see if it behaves with a load on the input.
An example of how some manufacturers can ****** things up, I have been helping my plumber friend fault find a new Grant combi oil boiler. For years Grant used the same basic controls on their boilers, just a couple of relays. they were reliable and simple. Hardly ever went wrong, but if they did they were simple to fix.
But now the new one has replaced all that with a board of electronics. It doesn't work and there's no information to fault find it, so Grant's own engineers are coming out to sort it.
If you have a proven reliable design, why mess it up and replace it with something new and risk the reputation of the company?