On this website, it says that cross pollination between two plants won't show up in the fruit of that year. I planted my zucchini next to my yellow squash. I had three zucchini come out half green and half yellow, horizontally split. The flavor was somewhere between the two. So if your site is correct, this is impossible. It would have happened the year prior and the mistake was made by the nursery that grew the seedlings. And if it was the seed, shouldn't all of the fruit from the plant have been the same? I am very curious.
Sometimes a plant will "throw a sport". Many new cultivars are simply sports of an older variety that "threw a sport", and a plant/seed company thought it had potential commercial value. For instance, "Jingle Bells" poinsettia is a sport, and Hosta "Revolution" is a sport. This is a natural occurrence that may or may not be stable. Your squash sported a bicolor zucchini, it is possible that this may occur again on that plant. If a plant is crossed with another, and the seed kept, germinated, and planted, the fruit from that plant will be the cross. The fruit from the original plant will be the same if it has not been pollinated with a different variety. Hopefully this did not confuse you more.