How did the FDNY not figure it out?

Something that bothered me about this movie...

As we see in the scene where Danny (Kim Cattrall) is alone in the Lynch apartment, Jimmy gets his nom du grafitti from his brother Terry's nickname "Turk" and his badge number 182. Now, Jimmy's activities become the main talking point of New York City. Isn't it strange that none of Terry's firehouse buddies put it together?

Imagine the following scenario:

Firefighter 1: Boy, that Turk 182 cracks me up. Y'know...Turk...that reminds me of Terry....

Firefighter 2: Terry Lynch, yeah, Turk. Hey, waitaminnit -- wasn't Terry's badge number 182??

Firefighter 1: You're right! Terry must be -- naw, hold on, Terry's in the hospital. He can't be doing this --

Firefighter 2: His brother! Jimmy! Jimmy is Turk 182!

I know, probably overthinking this... but it bugs me...