I didn't suggest a re-run of the original referendum, though a referendum on the terms of any deal (or lack of) wouldn't be a bad idea, if there was time for one.
The problem with your theory is that it can go both ways. For example, I know of a few people that voted to leave as a way of "sending a message" to the establishment that they weren't happy with certain policies and directions, but never actually imagined (or intended) that leave would win. A member of my family, in fact, was very anxious after the result came back - and after voting leave - saying they wanted changes in our relationship with the EU but didn't actually want leave to win.
I don't doubt there's examples that fit into both camps, and this brings us right back to my original point: we just don't know exactly what people wanted from their vote, one way or another.