The real question isn't to ask what sort of person would engage in this kind of petty scammer fraud, but rather who would do this to their own parents.

SecureFlight does match data and it is, in fact, why Pre-Check was first granted to FFP's of participating carriers (because all of the data was on file).

There is a risk that OP's parents get bagged and wind up dealing with the fraud issues when they thought that they would be flying somewhere, hopefully nice.