I think the term "adequate" is the problem. It doesn't say you need a certificate to operate a chainsaw, it says you must be adequately trained. The problem comes proving that they were trained and trained well enough. The simplest way for everyone to cover their bottoms is to have the piece of paper that says the person obtained the chainsaw training certificate. If a person has the paper work with dates and details of what was covered on training days that should be "adequate".
Maybe I'm reading this all wrong, but that is my take.
Wow a couple of responses came in while I was typing, I have no idea on the rules and regs about working around wires, I am just talking about chainsaws.