Perhaps my own personal example will illustrate the point I made about documented training.
This year the state began requiring proof that every contractor, and each employee, had received the OSHA 30/10 safety training. The trade association sponsored the seminar, and that save me mucho bucks.
At the same time, I took a job in a mill. This employer paid me to sit in class for two weeks of safety training. While the material closely paralleled the OSHA curriculum, there was no certificate issued.
In the second example, the training is documented only in the employers' files. It does not fulfill my requirement for the OSHA training. If I change jobs, I get to start all over again. Even if I request a copy of my personnel file, that will not meet the OSHA requirement.
This year the same situation arises with lead abatement training. Ours is a trade where we 'journey' from job to job. (Why do you think we're called journeymen?) Can you take your lead certification with you?
Ditto for asbestos.
In many situations, there is no such thing as 'employer certification,' either. Do you hire journeymen on their word alone? Data work that requires 'certified' work want that BICSI certificate.
On the flip side .... I know certain contractors that expect someone else to train their people. I even know of one "Big" franchise operation that promises to make your business a huge success - yet has zero involvement in training the 'techs.'
Personally, I believe that the employer has a duty to train his people, I also accept that simply trusting a piece of paper isn't enough. From the employees' viewpoint, though, if I can't take it with me, I don't have it at all.