There are lots of people who flat tow F150's but I believe they are all the 4x4 model which thru the transfer case can be put into neutral for towing. I don't believe the 2x4 model is flat towable.
Be careful about dealers. Many don't know jack about these nuanced details. Gotta find something written from Ford. The FMCA tow guide is a good start and I believe accurate. It shows only 4x4 model F150's are towable flat.