The parents' basis is not just the original cost plus improvements in the last 12 months.  It's the original cost plus allowable additions to basis since they bought it. 

Doesn't really matter if a gift tax return was filed because people like this aren't worth enough to pay gift taxes.  And you don't need the FMV at time of gift, in any case.  

Why didn't the parents sell the house tax-free, then gift their son the cash for buying the home he really wanted? Maybe it's none of our business.