@allenJo - I don’t think they need to step on any toes. The coordinator is there to make everyone’s job easier. It just depends on their specific job function.
I worked as a training coordinator for a company once, and I had to compile a list of company courses, and schedule trainers and classroom instruction dates.
I had to email other employees to find out when their best availability would be to meet for training, as people had meetings sometime or had vacation scheduled.
It wasn’t a big deal. Yes, I had to be aggressive but I don’t think I annoyed anyone. If feathers did get ruffled I would just punt back to my manager, and he would make a few phone calls to smooth things over.