While you say no disrespect is intended, it seems that your previous comment in this thread lends one to believe that I have an ulterior motive. Believe what you want and travel how you want. But to answer your question, I have heard of too many incidents around the island involving tourists, even though one is still too many.
Negril is a rather small town with a population hovering around 5000 and receives lesser numbers of visitors to the island than MoBay or Ocho Rios, so the number of incidents here are relatively small. But there have been incidents reported all around the island, in Hanover (not Negril), several in St James, a few more in the north coast areas and of course Kingston.
There are visitors to Negril who everyday rent scooters and feel perfectly safe and "in no danger" as you state you feel about the route taxis. There are scooter rentals all over Negril and tourists do rent them. But this month alone we have seen and talked to 4 sets of visitors who gotten serious cases of road rash which put an obvious damper on their vacation. All professed to have rented them in the past and knew the "runnings" and yet they ended up hurt. Bad things can happen to good people.
As I have stated, the majority of route taxi operators are hard working, honest and decent drivers trying to make a living. But you, as a visitor, do not have the years and years of daily experience with the route taxi system that all Jamaicans living here have - it is second nature to them. They instinctively know which taxis to use and not to get in, they were taught this as a child. There is no visitor to the island that has that same ability, and sometimes that even fails experienced Jamaicans.
So, by all means, go ahead and think you are in no danger at all using random route taxis. They are not allowed to refuse you, it is against the law. But would you have known not to get into the Lilliput route taxi? Would you have even noticed the Lilliput wording and known what it meant?
There is a system that has been put in place by the Jamaican government and JTB to directly serve the needs of those visitors to our beautiful island.
I can no more recommend that visitors use the route taxi system, which was designed with the local populace in mind than I can recommend walking through the unlit areas of the beach at night.
It is simply not wise advice.