Per TMZ...(I know)..you are correct about that woman part. She thought it was someone else's kid.
"We're told ... when Adrian was first informed about the matter, he didn't question the possibility he was the dad -- but rather asked how he could help the situation.
Sources tell us ... a few weeks ago, A.P. started to plan a trip to South Dakota to meet the child for the first time and he was supposed to fly out later this month.
...
We're told Adrian met the child for the first time while the boy was on life support."
http://www.tmz.com/2013/10/12/adrian-peterson-son-paternity-south-dakota/