The Wikipedia account of the Andrea Doria details how many survivors each of the large rescue ships picked up. Nothing about one guy getting fished out of the water by a fishing boat that made it up from New Jersey. You should add that to the Wiki.
Also provide details about your grandfather’s hydrofoil fishing boat,
It was 60 years ago, but I’d swear that I saw a dozen or more small motor boats with one or two survivors each. It’s a good thing this all happened in the summer, there could have been more casualties if the water was cold. Also, the survivors were deposited along the nearest beach and greeted by hundreds of people who were waiting with coffee, soup and blankets.