And they sure as hell won’t know what they would have wanted to want in 20 years time.

That's the same thing

No it isn't, maybe python is clearer:

    not think(many({
        knowswhattheywant(p)
        for p in people
    }))
    !=
    think(many({
        not knowswhattheywant(p)
        for p in people
    }))

This just isn’t how the semantics of the English language work

The sentences have different meanings.

"I don't think a lot of people know what they want." -> I believe it is a rare trait in a person to know what they want.

"I think a lot of people don't know what they want." -> I believe it is a common trait for a person not to know what they want.

These things are not mutually exclusive nor mutually inclusive.

Lots of similar sounding statements are subtly different like this in English. "I am not happy" and "I am unhappy" have slightly different meanings as well.