Nothing sounds unusual about your story; it sounds like you had sex and then got a period, then got pregnant the first week of September, thus, the due date of June 1. That matches up with your last period being August 25, and the 6w3d count they gave you on October 6. What is bothering you about it?
Have you had an ultrasound by now (I assume so?) Once they measure the baby (crown to rump) and check other developmental markers, there is no room for doubt. If the size of your baby had not matched when your period came, the doctor would have changed your due date, not ignored the difference because of when your last period came. (Doctors don't say, "Oh, the baby looks a month further along, but forget that -- you had a period." After all, the doc is looking at the actual baby there on the screen. ) Once you have an ultrasound, the date when your last period came is just a historical note in your medical record. If they didn't say anything about changing the baby's due date, you can assume the ultrasound info matched what you told them about your cycles.