Wrong.
Not declaring your modifications will only affect your side of a claim, it will not affect any 3rd party payouts. Fully Comp covers damage you cause to others, as well as damage caused to yours. If your car is not as you said it is, they can refuse to pay out to repair it, but they will still have to pay out to repair any damage you cause to others. It doesn't make your policy void, but it could effectively make your insurance the equivalent of 3rd party only.
This is quite misleading advice.
What an insurer can do is restrict the cover it provides to that required by the Road Traffic Act - which you allude to in your post. However, if they feel that they incurred costs meeting a claim which they should not have had to pay out on they can recover these costs from you through court.
Bottom line is that you could end up facing the full bill personally, though to the person you crash into, everything would appear as normal.