This is exactly what my employer did with me and the other engineers.
We essentially had a 1 day course, we skipped the theory as the instructor simply said 'you know more about forklifts then we do' (fair play to him).
He tested us on counterbalance, reach, telehandler, order picker and a 12tonne capacity counterbalance. Basically just drive round the building/workshop/yard without hitting anything.
It's stated 'for maintenance and testing purposes only'.
But I agree, your service engineer should have some record of operating training, albeit not a full operators license.