I know I've seen in the news this year, a couple articles about females sexually harassing or assaulting other females. Same with male on male.

So how exactly does your company think having an extra person in the room, just when it's opposite sex, is going to insure anything?
If they are that paranoid, then like was said earlier, they need to install cameras & mics in the meeting rooms and offices. Put up the little signs about being recorded. And carry on.

The question you should be asking: How do I turn this into a business opportunity. Because I just got done putting in 16 cameras & 4 microphones for a small business, that has become a little paranoid about this very thing.
You need to get you wife to tell you who to talk to there, and approach them about an "employee monitoring system" :)