I dislike it, too.
...not because it is an Americanism. I dislike it because it implies a level of parental control that I find distasteful in all but the very young.
The implication is that the parent has selected a suitable 'play-mate' for a 'play-date', in the manner of an arranged marriage. This is ok in toddlers, but my children are now of an age to choose their own friends.
Certainly I don't approve of all choices, and refuse entreaties (usually from feral 9 year old) to invite be-mulleted members of the local Young Arsonists club to play in our house. Well, I at least get them to check their matches at the door...