I decided to stick with Cait as my companion, the first thing I did was get her a sequined dress, sunglasses and a sea captains hat. Now that she looked a lot more presentable (even a bit cute) I decided to cure her chem addiction. After she sat in the chair I was presented a view I wasn't expecting.

Yes I took a screenshot,

I don't think its appropriate to share it tho, you want to see? Do it yourself.

Yes, I'm sure she is wearing underwear. Every NPC essential or not, even our character, is wearing underwear. I remember killing Father and stripping him of his outfit. Even he has underwear.