If you want to get technical about it, most (if not all) of the 16-3's were put together using spare parts and donor frames. Of course, this was done by the factory, not by individuals. Every single 16-3 I have ever held or seen has had a "6" stamped over a "4" in the model number as pictured.
As mentioned before, with only 3630 produced from 1947-74, the K-32/Model 16 was never very popular. By the time the -3 engineering change was made, orders were probably so rare that the factory didn't even bother to stamp dedicated Model 16 frames. When an order was received, they just overstamped a Model 14 frame, fitted it with a .32 Long barrel and cylinder, and out the door it went. Just my theory...