I'm with isis on this one, positive. If the birth time has been recorded as 6:10, why choose a time as much as 7 mins earlier? In my experience of speaking to mothers about the birth times of their children - and this includes my own experience after giving birth - hospital staff may wait until a child is breathing properly before announcing the time of birth. On the other hand - as was the case when my own were born - the hospital staff were chatting away to me about the baby, and almost forgot to mention the time of birth!! Fortunately I wore a watch to each of my kid's births, and checked the time as each left my body.
Gemini ASC can be a lot of things - it expresses itself quite differently in different people. I can remember being incredulous when I discovered that my former sister-in-law had Gemini rising, because she is quite serious and hard-working, with very little to display of her Gemini self. Firstly I checked that her time was correct; it was, and here in Oz the correct time of birth is to be found on hospital records. For her, Mercury is in the 10th and in Pisces, so this dampens - even hides - her ASC considerably. However, she is very intellectually oriented, and laughs gently - but not often - doesn't overtalk like many Gemini Asc's, but can multi-task like a true Gemini R. As she has passed the age of 60, she has also proven herself to be a student-for-life, something which is common in those with Gemini ASC.
positive, you have to consider your Mercury placement, and how that is placed. In Scorpio, conj Uranus and in the 6th will give your Gemini ASC - should you have one!!! - quite a direct, analytical and organised, but electrical/inventive - expression of self.
Just following an idea.
PS: When I first discovered that I had Cap ASC - and what this meant - I did not believe it at all. I had always seen myself as very open and out-going. Others do not; they see me as guarded, serious and responsible. Who knew?