Could well be. I'm currently on my 3rd PCB (original + 2 replacements) on a 7 year old Baxi Solo 3 (it's the same PCB fitted to the Solo 2 & Solo 3) and the one I've got now suffers from "chattering relay syndrome" on the pump overrun. One of my failures, including the "burning"was exactly as you describe and a new PCB sorted it.
For some reason, your gas valve is not opening to feed gas to the burner, it could be the PCB that controls it, or it could be the gas valve itself, or even the wiring to it. (the engineer should be able to test for this though) However if your PCB's "burnt" then if it hasn't failed yet, it's well on the way, I would replace it anyway before we hit the real winter weather.
The price sounds about right, the PCB alone costs over £150 I seem to remember, seems ridiculous to me for the few cheap components on it.
Personally, being on my 3rd PCB, I think it's a deliberate ploy by Baxi to fit substandard PCB's to their boilers that are not suitable for the duty and then make a small fortune on the spares. These days other far more complicated electronic circuits in cars, TV's, security systems etc., have a life generally well in excess of 10 years. The burn marks on the Baxi PCB say it all really..IMHO