I shy away from calling not-legit: even the ability to do so is a fundamental threat to the Beeminder model.
I really like the fact that I can tell Beeminder e.g. “I’m going to do such-and-such 3 times per week or pay $5”, and then that is locked in. I either do it 3 times per week, or pay $5. No other possibilities. (This, of course, vastly increases the chances I’ll do it 3 times per week, because otherwise I’d have to pay $5, and no one likes giving up money.)
The fact that this is so clear-cut is what makes it so valuable (to me). No excuses, no getting out of it. 3 times per week, or $5. (Or whatever other numbers there are for the goal in question.)
In theory this could work with fineprint, but in practice there is no way it could. The second it becomes that bit less clear-cut, the akrasia sets in, and much of Beeminder’s value is lost.
I think this really is a difference in how the akrasia manifests: you say you have a hard time doing things where the deadline is not today, but have no problem navigating a complex system of exceptions. I, on the other hand, mostly have no problem in being motivated a few steps further away from derailment (the difference in buffer between “I have to do this in 7 hours” and “I have to do this in 2 days” is quantitative, not qualitative, even if Beeminder’s UI shows them differently), but would have great difficulty in getting myself to follow a complex and semi-arbitrary series of exceptions and fineprint.
Anyway: I’ve called not-legit exactly once, in ~6 years of using Beeminder, for a medical emergency. If you have to visit the emergency room, or something of a similar level of outside-the-normal urgency and unexpectedness, then sure, my philosophy can accept that that’s what not-legit is for. Basically: for something so outside the bounds of normal life that it throws everything else completely out the window.
For me, I don’t know if there is much else other than a hospitalization or emergency room visit that qualifies. Maybe if I was stuck somewhere because of something like the 2010 volcanic ash cloud or something along those lines.
But I also know that my reading of this philosophy is fairly strict: someone else who was practicing more or less the same philosophy might treat lesser-but-still-out-of-the-ordinary events as triggering a not-legit, such as a car breaking down or the like.