I'm not a tree guy, but I have had experience in vertical ropework, both recreationally and commercially.
People use ropes to get to places normal people can't reach. If you get into trouble in a place you needed ropes to get to, don't assume that others can help you. The difference between a victim and a rescuer is their ability to work in the accident environment.
The vert rescue squad at the fire dept may not be much use for tree rescue - all their training might be focused on having a solid accessible support ABOVE the victim. This assumption of an accessible anchor point above the victim is fine for building sites and cliff rescue, but not so good for trees.
The vert rescue squad are likely to be part timers (with other fire service duties) so don't expect them to be awfully proficient when taking on rescues on the edge of their experience.
Time is also an issue. If someone has been hit by an object or cut by a tool then the rescue needs to start immediately, not in an hour's time.
Tree guys spend their whole life in trees. They are going to be 1000% better moving around in trees than a fireman. If having two trained climbers on site is commercially impossible, then I'd make sure that your groundies have the mobile phone numbers of other climbers who work in the same area.