Apparently in some airports Southwest has been able to convince the TSA management to police the elite line requirements, and in other airports the TSA management has refused to help. The latter is disappointing.
This is how it is in TUS as well. Walk up, show the TSA'er your ID, A list card and BP and you're thru, with your own dedicated x-ray machine with no fuss, and practically no waiting. I was through security in less than a minute last week when there was a good 20 minute line. It is shared with the crew and disabled people line though, so if you're stuck behind a wheelchair it can take a few minutes.