After consulting with an friend of mine (NYPD), it's illegal but with a double-edged sword type of illegal. As known, people no matter what will listen on to radio chatters of various channels. But to record and distribute is highly illegal without authorization, meaning a signed legal document stating it was allowed. Thus also forging such documents are also highly illegal.
The person you were talking to may have said it was fine, but you probably misunderstood the statement as they wouldn't know if you were listening to them or not over their channels; unless they were really cracking down on you. I still highly suggest you do not record and implement them to a route.
Another note, you said you contacted the source of recording? Unless the source was approved by the FCC or FCC themselves, I wouldn't take their word for it. Remember, in most cases like these, FCC rules over whatever rule MTA might allow or disallow according to radio transmissions.