
Why doesn't she just say that she slept with other men and got pregnant from them....

Hmmm, it's more that it means she acknowledged that she spent time with someone at that night which coincides with the fact that the emperor had done the same thus giving him some excuses to do all kind of things openly. And he's not known for being benevolent.
Normally, best case she'll get kicked out of the force, worst; execution for various reasons.
Who's the grey family again?
Asshole family of fl???