That doesn't seem right. I went to a state school. I think CS grads had a marketed 90ish% placement rate. Talking to others in my classes right before graduation it seems we had at least 80% of people with jobs lined up prior to graduation.
There are about 65k CS undergraduate degrees issued each year.
I don't think the BLS is double counting jobs. I believe they go to the companies for that info, not random job boards.