Generator transfer switch manufacturer compatibility?
No, he is full of it. A transfer switch is just a switch. Kohler doesn't even make the switch they sell, neither does Generac. In fact the switch mechanism inside of them is the same (the electronics are different and they use different brands of circuit breakers).
The only issue is that the wiring diagrams likely show you specific connection references for their own respective brands. But anyone with half a brain can figure that out.