Let me start by saying I have a two month old 2014 HyTi with 4500 miles on it and I have filled the tank 10 times now. I see the same fuel gauge discrepancies as everybody else.
1. Cold weather isn't the problem. I'm in Southern California and for a month in my area the daytime temps have been in the 70's and 80's.
2. I have used remote start 3 times since I have had the car, each time less than a minute.
Now for my opinion.
acdii you partially solved some of my discrepancies and gave me a theory when I viewed your photo in post #4. I had never seen my fuel gauge display over "Full". When I saw your photo I said "the next time I re-fuel I'm going to continue adding fuel after the second fuel nozzle click off". Usually if I stop fueling at the second click the fuel used indicator and the gas station pump are within .5 of gallon. But this time I added more than a gallon difference for a total of 12.84 gallons! (I had driven until the gauge wasn't even showing red.) After this fill up my fuel gauge was above full like yours in post #4.
OK so here comes the meat of my story.
On the next fill up I went to a different gas station than the previous fill. (I alternate between the same two gas stations on my work commute. One in my home town and one near work.) The fuel gauge had just turned red but I had to force in 11.11 gallons after 4 click offs! That did not seem right to me as the fuel used indicator was showing 11.35. The fuel gauge was NOT past full after this fill up. Alright so the next day when I started to work, after just 15 miles my fuel gauge was showing a black space below full! After 48 miles the fuel gauge was at 3/4 full! My conclusion was, at this gas station in my home town, the car must not be on level ground AND THE FUEL TANK ISN'T BEING FILLED TO CAPACITY EACH TIME. (Caps for emphasis and not yelling) Didn't I read somewhere that the Fusion fuel filler doesn't enter at the top of the fuel tank?
So IMO the discrepancy exists because the fuel tank isn't being totally filled after each re-fuel. Examples:
Tank A - Assumed full tank. Total miles driven - 430. Fuel Indicator - 11.5 gallons. Actual fuel added - 11.5 gallons.
Tank B - Assumed full tank (Added 11.5g from above). Total miles driven - 430. Fuel Indicator - 11.5 gallons. Actual fuel added - 11.0 gallons.
Tank C - Assumed full tank (Added 11.0g). Total miles driven - 430. Fuel Indicator - 11.5 gallons. Actual fuel added 12.5 gallons. (Why? Because Tank "B" wasn't really filled to capacity).
Tank D - Actual full tank! (Added 12.5g). Total miles driven - 430. Fuel Indicator - 12.0 gallons. Actual fuel added 10.8 gallons. (Either the car isn't level and the tank isn't full AND/OR you stop at the first or second click and that isn't filling the tank either).
Remember the fuel used indicator is clueless as to how much fuel is actually in the tank. You could drive 50 miles and then reset the Trip Mileage and that would mess up your fuel used. Therefore I take the fuel used indicator as a close "estimate" and not necessarily an "exact" fuel used. You discovered that with your remote start findings. Here's a test. Does the fuel used indicator increase if the ICE is running but the car isn't moving regardless of remote start? I haven't really took notice if it does.
Needless to say the odd fuel filler design, the strange "all over the place" fuel gauge, and the fuel used "estimate" make for some stressful times in knowing how much fuel is really left in the tank.
Hopefully what I wrote is understandable and sounds reasonable.