Precision is indeed a most important factor. I go to Church on Sunday mornings and to a bible study on a Tuesday and the route is a local one so gets gobbled up (in my mind) with the generality of local trips: I visit other places locally more frequently than church.
1) Pure chance: 1/50,000,000 is improbable. Agreed. But it can happen for all that
2) A pattern of refilling. You were right to investigate this - given the frequency of return from work related run-outs (not all because I don't know but it appears likely that most if not all were). However the pattern would involve a specific and repeated level in my tank which culminated in me taking the trip to work, forgetting to fill at the latter stages of the in journey and forgetting all the way home. This could happen and happen 6-7 times no dbout. Except that I couldn't see anything that would prevent me running out when the same tank level conditions occurred elsewhere. Its a long route, you don't remain sleepy on a bike in traffic for long. I have forgotten at other times and remembered in the nick of time. Why under these particular circumstance? I can really see no reason for it.
3) Again, the bare bones indicate some merit in this. But as I've said, I don't know that precisely how much I have left. If I catch the needle hitting the stop then I know what I have left - but again I wouldn't be eeking the last mile out of it - it ain't that accurate. But in general I have only a rough idea of where I am in the quarter tank and wouldn't be gambling in a crazy fashion. Note that I only forget a relatively few times from the total filling pattern. I want to fill when I'm as low as I can but I'm not anal about it. That I run out so infrequently shows that I am by and large playing safe all the time. I would usually not fill before the needle hits the stop and manage the margin correctly to get the max out of the tank before refilling. Except when I forget.