My experience with cabs (though I have not done this route) is that if you see a sign about fixed rates then you should ask the driver before you get in if it is a fixed rate. If he says no, ask another one. If it seems unusual, look for some klind of authority to ask.
I have had many cabbies try to tell me it isn't true when there IS a fixed rate.
Cabbies, - you gotta watch 'em.