I just went through this a couple years ago. I was taking an anti anxiety med and indicated this on the 3rd class medical application. The FAA doctor told me i can't take this type of meds and said I would be denied. Of course a few weeks later, I got the denial letter in the mail. I think it came via certified mail so quite official. I went off the meds and waited 3 months. Went and saw my family doctor and had him write a letter stating that I was off the meds for 3 months and that I was doing fine. I sent this letter to the FAA and within 30 days I got my medical certificate in the mail. They didn't question anything. Once they had the letter, they issued the medical. I did follow up with them on the phone once or twice to make sure they got the letter and if there was any issues with it. I finished out my PPL last year and have been flying a Cherokee 180 ever since. Loving it.