Competitiveness brings out interesting facets of human character, doesn't it?
Naturally you want your golf events to be fair, and when fairness comes into question from a participant, you want to have a legitimate answer. Handicapping is meant to level the competition*, so naturally the question regarding fairness might be whether the player Indexes or Course Handicaps are correct.
Assuming that players of the same gender are competing from the same set of tees*, there's an easy, if inconvenient, solution. Provide the griper(s) with their most recent 20 scores (or as many as they have accumulated) and a couple formulas from the USGA with which they can calculate their Index and Course Handicap.
To calculate a course handicap for the course on which a tournament is played, use the formula: Course Handicap = Handicap Index x Slope Rating / 113
Assuming they have done their math right, their result should confirm the Index and Course Handicap calculated by your service or software.
* Note that handicapping "levels the playing field" when competition is men vs men or women vs women on the same set of tees. If players of the same gender are competing from different tees or players of different gender are competing from the same tee, there is an additional adjustment.