If "the fan fuse" means the fuse built into the Fantastic Fan, there must have been power supplied to the fan to burn out the fuse. A circuit which cannot supply enough current would be a problem, but this circuit used must have been able to supply enough power. I can see how reversed wiring polarity might blow the fan fuse when it triggered on, but unless Casita
is doing things very strangely the white-to-white assignment seems reasonable.
If it were my trailer, I would use a voltmeter to confirm that the pink wire is +12VDC relative to the white wire, and confirm in the fan installation instructions that white is ground and black is power.
I would also try taking the fan off (I assume it readily lifts out of the permanently installed housing, like the MaxxFan), taking to a power source (the battery), and temporarily hooking up power (wires with clips or whatever). If it doesn't work there, it's not going to in the ceiling, and maybe it's defective.
My fan is MaxxFan, not a Fantastic Fan, but I would be surprised if I could not trigger the fan to run by just turning the thermostat knob cooler, even at 50 deg F. The factory specs say its range is "20 degrees F to 120 degrees F".