It does sound like there was an issue with the ticketing. My guess: reservation was made, reservation wasn't properly ticketed / payment didn't go through, as it was close to departure the reservation hold on the seat/inventory "expired" or proper ticketing missed the deadline, and so boarding was denied. IMO counter agent should not have given BPs if it wasn't properly ticketed yet.

It would be really bad if there is no indication there is an issue on the BP, not even "flight coupon required" or similar notation. Javabytes asked this specifically but it went unanswered by OP. I don't expect any flyer to know "flight coupon required" on their BP means there is a serious issue, but it would be comforting to know at least something on the BP was off.