I also have to add that during my early sonogram we got measurements from 8 weeks 5 days to 9 weeks 3 days. We went by the largest measurement we got. But in all actuality my baby really could've been conceived 5 days sooner than the measurements showed.
If the boyfriend is all that worried about it he can pay for a DNA test.
Relax- dates can be off by a few days! When the doctor says your conception date was June 1st, it is JUST AN ESTIMATE. Also, take into consideration that implantation can take 7-12 days past ovulation, so your little baby probably implanted earlier than usual, hence the reason they are measuring bigger.