The Perverted trait might be responsible for them asking to meet in those rooms, but it doesn't seem to be the sole decider in whether they will ask you to follow them there. I've got a Highest virtue, non-Perverted
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that will sometimes ask me to follow into those rooms, and then she'll slap me right after. Her traits for reference are: Competitive, Scheming, Evil, Deaf. It's possible multiple traits allow for that behavior, or it's just entirely random what room they pick to go to.