That sounds like their local audio routing scheme isn't switching to the locally recorded-whatever.
Stations handle this workflow/process differently: Some will have their station automation send a GPO command (general purpose output) to an audio console fader channel to mute the incoming network, or in this case, another station' programming when a local break is supposed to run. At the same time, another GPO triggers the local automation to play-local-whatever via a different fader at the same console. The problem with this process; is whomever was the last person manually running the board (console) must properly set up the console with the proper faders up or down before they leave for the night. In my example; if the fader(s) for the local break aren't left up, or the wrong faders up or down, one could easily get this sort of thing happening.
The other way stations do this sort of thing; is by using a in-house core audio router, or a small separate router which the local automation turns various sources on or off when triggered by the local automation GPO.
Of course the third possibility; could be they're having intermittent break triggers being sent down the line from the NYC station. If the local automation doesn't hear a trigger, whatever audio coming down the line stays up locally with no local break being triggered.
These last gremlins mentioned are a bitch to troubleshoot sometimes, because they're so intermittent. Unless one has access to very expensive network monitoring software like Splunk!, the alternative (pardon the pun), is to have their one engineer camp out all night to see if they can catch it happening. That's assuming of course it happens when you're sitting at the station those particular nights.
