Can't say much about cross training in most dealerships, but this is what i hear from the tech's I've run across from the local Hyster/Yale dealership. Both trucks are virtually identical. Some of the software is a little different in the VSM or ECU. The Hyster training they received directly transferred to the Yale. Except for technical stuff, programming and the like, any good tech can fix any lift truck.
On the other hand, the salesman said He would go in and quote a Yale, and the company would send the other salesman to quote the Hyster. In a sales mode, I would think multi brands would be a conflict of interest.