In the situation you described, I definitely wouldn't allow the child to be there. That just sounds fishy.
But in general, if a child were invited over to my house for a playdate, I wouldn't expect, or want, the parent to remain there, hovering. If you don't trust the parent who's hosting enough to watch your kid on their own, you probably shouldn't allow the kid over at their house to begin with.
I don't know if this is how it still works, but when I was a kid playdates were spent playing dolls or ponies or imagination games in my friend's bedroom, basement, or in the backyard . . . The mom of the house would be easily accessible, but not staring at our every move. (This is at age 8 and up I'm talking about, not toddlers or REALLY little kids.) It seems like a good system to me.