Ds upset while I was telling our birth story
Yes, it is 100% coincidence. 6 months baby does not have a cognitive ability to understand stories, birth or otherwise.
6 months old get upcet often. Gas, teething pain, as visceral gut reason to your own mood. If you feel that the birth was not "perfect' because it was hospital and not home, he could have picked up on your anxiety. Perhaps, you should re-frame the story for yourself or refrain from talking about in anxious or upset tones. Babies pick up on emotions, not meaning of words at this age. 6 months does not have cognitive capacity to have a memory of birth either.
He was most likely responding to the stress in your voice but I did observe an interesting response in my 1 yr old niece when she was in the room while her birth video was being played. It was her first birthday and she was walking around the living room interacting with various family members. Her dad had turned on the video he shot the day she was born. During the part after she was born, she would occasionally glance in the direction of the screen when she would hear the baby on the TV cry. However, when it got to the part where her dad was filming the nurse giving her first bath, and the baby (herself) was crying again, she immediately went over to the TV and was trying to turn it off. Coincidence? Possibly. But that specific crying scene upset her whereas the crying scenes prior hardly elicited a response. Was very interesting to observe.