But it's from the "dairy" section of the supermarket! (I have heard this. I'm not lactose-intolerant, but my SO is, and I was talking to someone about lactose intolerance and how remarkably decent Breyers' lactose-free vanilla ice cream is... and it came up.)

By this person's logic, other things that are dairy are: pre-made Jello gelatin cups, orange juice, bagels, "natural" peanut butter, shredded potatoes, and cans of whack-a-biscuit dough. They're all in the same aisle in my supermarket, and some are closer to the milk than the eggs are.