I think most tradesmen prefer to use their own tools. I play an electrician on TV and use my own stuff except the battery powered tools. Even then I make sure the boss gets me what I want. Union guys have to run whatever their employer provides, at that’s how they run from the hall in Seattle.
So, for some things I’ll let the employer provide tools. But for others I use my own and would trust what they provide. The most important for me is a meter or hot stick. I rely on those so I don’t get hurt. So it makes total sense that an arborist would want their own climbing by gear even if they are working for someone else. I guess the same could be said about the saws you use also