Contrary to the question's premise, Palm Beach Gardens is a genuine, incorporated city in Palm Beach County, Florida. Founded in 1959 by insurance magnate John D. MacArthur as a planned "garden city," it now has a population of ~60,000 and covers 56 square miles.
The city features a vibrant downtown, the PGA National Resort (host of the Honda Classic), high-end shopping at The Gardens Mall and Downtown at the Gardens, top-rated schools, and extensive parks and golf courses. It is a fully functioning municipality with its own police, fire, and administrative services—nothing "paper" about it.
The term "paper town" usually refers to a fictitious map entry or an unincorporated placeholder; Palm Beach Gardens is neither.