One alternative is to get two bids to repair the structural issue and that alone, ask for that amount to be knocked off the price (not cash, they hate that even though it’s all the same). In writing, inform them of the issue and your request (now they cannot tell the next guy they were unaware), maybe even threaten to tell the next guy if it goes down that road. They have two choices, accept your discovery and new price or tell you to pound sand and go to #2 on that list, seems like you win either way but you need to be prepared to not get that house. BTW, how expensive/extensive did your inspector say it was?