Could simply have been miscommunication as often happens when messages are passed between OpenReach, BT Wholesale then the ISP.
The problem is stated as not being at the cabinet, ports are available, but rather at the exchange and that no port is available
The response is often about ports at the exchange when they actually mean the street DSLAM.
Could have been something as simple as a line card fault meaning no free working ports were available.
The original reason given might have been correct, just the location of the ports in question being wrong.
I'm with you on wishing the initial info given should be more accurate.