Their claim of lawyer saying you’re liable may just be them seeking to further rattle your cage.
Good point. Their “lawyer” might just be someone in the pub who knows someone whose brother-in-law’s mate is a conveyancer. Ask for a copy of the lawyer’s written advice so that you can give it due consideration.
However, if there is a record of complaints about the condition of the hot wwater system (including rust particles in the water) you might be liable due to negligence, as suggested in Kaindub’s post above. Hot water tanks can have a discreet lifespan after which the bottom can just drop out of them, but there may be signs they’re getting to the end, with particles in the water.