Excellent question, Ron.
Quoting from the TR3650 description (Ford shop manual): "The reverse gear operates through a constant-mesh, fully synchronized system".
Quoting from the TR3650 parts breakdown: Item 35, P/N 7124 - reverse gear synchronizer assembly (consisting of item 37 spring, item 38 hub, item 39 insert, and item 40 sleeve).
So, is the Ford Mechanic lying to you? In a word, No.
The method I desscribed is not the only way to synchronize gears. There are several others I know of, and transmissions may use some or all of them, sometimes even 2 different methods in tandem. Some of these methods are known by purists as brakes, clutches, dogs, spline rings, etc. They reserve the term "synchro" for just one element in one particular method. They would insist the TR3650 has a reverse clutch or brake instead of a synchro, even though all 3 perform the same function.
Similarly, if I ask you if you own a sports car, you might say yes . . . while your mechanic might say "No he doesn't, he owns a Mustang". Depends on if you consider a Mustang to be a sports car.