The vendor is wrong. You only need one UC100.
Mach3 licenses are not tied to anything. You can run as many copies as you want, with as many machines as you want, with whatever controller you want. Technically, this is for hobby use. If used in a commercial setting, you should buy one Mach3 license per machine.
Mach4 licenses are tied to the PC.
UCCNC licenses are tied to the UC100 (or any other CNC Drive controller)
I would highly recommend a UC400ETH rather than a UC100. It's only about $25 more, and offeres more I/O, and is more powerful, and has much better noise immunity.