LoglineCommander Una Chin-Riley faces court-martial along with possible imprisonment and dishonorable dismissal from Starfleet, and her defense is in the hands of a lawyer who’s also a childhood friend with whom she had a terrible falling out.
You generally can't make people incriminate themselves, and upping a charge from fraud to conspiracy would be exactly that. That is, in a court run by laws instead of TV logic she could've remained silent.
...unless there's some special sauce in US law that says "once you take the stand" or something, dunno I don't speak common law and Trek can't help itself but assume US law but it definitely doesn't look kosher.