I think validation is more about whether or not someone will pay for your solution than if it actually solves the problem or not. Sounds like the same thing, but it's not really.
That's correct. You might have invented the "better mousetrap" but no one might want it. Product, yes, market no. You don't validate the solution, you validate the market. The market fit is the solution fit with the market, not that you have a solution that the market doesn't want.