So most airports have "elite" screening lines for first class passengers, and elite FF members. Who pays for those? The airlines?

I'm specifically wondering because I was at MKE this past weekend, flying AirTran in first class as an elite A+ member. I went out of the terminal that's shared with Northwest, which has its airline club lounge there. There's also an elite line, though I forget if it was marked simply 'elite and first class' or 'NW elite and first class'.

Anyway, since it was slow the elite 'boarding pass checker' was checking non-elite boarding passes as well. She checked mine, and I started toward the elite line. She stopped me, and I showed her my boarding pass, and how it said 'Elite', and pointed to my first class seat assignment. She looked confused so I confidently walked back to the line, and I heard her asking a supervisor about AirTran but not the answer. I didn't get pulled from the elite line (which was a lot shorter), though.

But was I really allowed to use that line? Did Northwest pay for it? Do you have to look for airline emblems on the elite lines? Or is it some TSA-funded thing and the airport decides how to use it?