I don't know the details of what year Fit you have, but I just looked at several websites on Google that indicate that at least the 2009 Fit, manual or auto, can be towed four wheels down according to the Honda manual. If it's an automatic, you have to go through the running through the gears in a specific order, holding your speed to 65 mph, and redo the preceding after 8 hours of so of towing. You need to look at your owners manual and see what it says and maybe look at the annual Motorhome magazine towing issue for the year of your car, but at least some years can apparently be towed.
Jerry