If an ultrasound in your eleventh week said you have a due date of July 7, it does indicate you got pregnant around the 13th or 14th of October. (When was that ultrasound, around December 16?)
Having a period on September 29 also indicates that the guy from the 23rd is not the father, because not only do your periods stop when you're pregnant, but September 23 is too close to the period for you to have been ovulating then. Besides, the ultrasound saw and measured the actual baby, and placed conception in the middle of October, not September, based on the baby's size and developmental markers.
When a patient comes anxiously at a doctor and asks them to guarantee something 100%, if the doctor's conclusion has to rely in part on the patient's story, they can't guarantee the thing 100%. Patients forget stuff, omit stuff, get dates wrong, etc. She heard you asking her to guarantee a conclusion 100% that comes partly from hearsay (from you). Every doctor has been burned by a patient telling them inaccurate things or forgetting important details, then coming back and yelling at them (or suing them) for something they said based on the patient's input. All a doc can guarantee is what she can prove medically. What she can show medically is that the baby was conceived around October 13. She can't guarantee your part of the story 100%, even if you know it's correct.
That said, I think what you were trying to ask her is, "Can sex on September 23 produce a baby conceived on October 13?" She would probably have been able to tell you sperm doesn't live that long, and sex with one guy in one month does not have an effect on the results of sex with another guy in another month.
Again, remember that the ultrasound measured the baby, and came up with a conception date two weeks into October. If the baby had come from the sex on the 23rd, it would have been much more developed.