DNA test question for a story

I've been trying to do some research for a story with the working title "The Nancy Boys and the Case of the Confused Chromosome".

In this story, the Nance (aka Nancy) Boys are showing how DNA tests work for a science fair project. The results of their test fall into the hands of the school principal, and the boys wind up having to dress as girls until they can solve the mystery of how they both show two X chromosomes in their DNA's instead of an X and a Y.

The problem I'm running into is I know almost nothing about DNA. Does anyone know of any way a test could show two X's, even though the subject has an X and a Y? I thought about just having the test results switched the the tests from a female, but if there's any other ways the test could have some kind of error, I'd love to hear about it. :)