Kilimanjaro has a rescueservice in the high camps - when they are there. The problem with Kilimanjaro is that the surrounding people are poor and lacking medical service, like Roger says.
To be honest I think, that people climbing Kili must take their own responsibility and pay for experienced, competent guides. Many people prefer the cheaper solutions, and get what they pay for.
When you go, bring your own first aid equipment, and leave what you don't use for the guides or the company. Be aware, that sick and injured people have to be carried by stretcher all the way down.
This is Africa and the ressources are few. We come as rich people to do something, that could seem "matter out of order" to the people who suffer from severe draft around the mountain.
I experienced another horrorstory earlier this year - when all the guides took action - and all the "white people" took off and left no first aid equipment - in connection to an accident at the summit..
Helle