When I was hired at Eagle (Oct 1995), we were measured in the interview, and anyone not meeting the height requirements was sent home. Period. No exceptions. Shoes had to be removed for the measuring.
I interviewed at NWA in Jan 1997, it was where I'd always wanted to work, I'd been waiting for this interview forever, and I wanted that job so bad. The interview was going GREAT, and the interviewer said that since my height was so close [to their 5'2" minimum] it had to be verified. They stuck me up against a wall where a post-it note had been stuck (at the 5'2" mark). Again, shoes had to be removed for the measuring. I was .5" shy of the mark. I was sent home.
The height requirement at the AA interview was a practical test, where we had to reach into a mock overhead bin and remove a fire extinguisher from it's brackets and put it back. I'd been at Eagle for 5 years at the time I interviewed with AA (Sep 2000), and had been teaching new-hires. I could undo a fire extinguisher bracket with my eyes closed. So not only did I wear 3" heels to the interview (I knew they didn't make applicants take off their shoes for this practical test) but I could remove that fire extinguisher no problem without having to be able to see it.
So, generally speaking, if there's a listed height requirement, expect that the company is going to be pretty stringent about it. Apply if you want to, like someone mentioned above
do not lie on an application, but expect to have your height verified at some point during the interview process. But don't surprised to get sent home from the interview if the height does not fall within their published requirements.