I think JasonWW's post answered some of question, possibly, that the current referred to was not just the led current, which I guess wasn't directly measured.
Yes, I get how the Vf curves for led's work below spec. The thing is, you don't care how much voltage is across it, only how much current goes through it. So it depends how it's driven. For example, if you drive a 1V led with a 10V source in series with a 100k resistor, you're going to get about 100uA of current. There's no way Vf is shooting up above nominal 1V, and it can't go below 0V. Either way between 90 to 100% of the 10V drop is across the 100k resistor and 9 to 10V across 100k fixes the current in series through both the resistor and the diode to somewhere between 90 to 100uA, pretty tight, without knowing anything about how sharp that kink is.
Ok, this gets worse when the diode voltage gets closer to the source voltage. So for a nominal green diode voltage of 2.1V and a source of 3V anywhere between 0.9V and 3V can drop across the series resistor. So that's a factor of almost 3 (pesimistically, if we know NOTHING about the kink). But even still a factor of three change in current probably shouldn't take the LED from being just fine, to presenting no light.
Ok, if the battery really is at 3V then the output of the mcu pin may be more like 2.5, so that starts to be problematic, now we have voltage rage across the resistor of 0.4V to 2.5V so > 6 times variation, but again, that's very pesimistically assuming these diodes can have 100% variation in performance and that's at the lowest battery levels. What was seen happened even with fully charged batteries. I can't quite rule it out entirely with this logic, but it seems far fetched to me that Vf fluctuation should cause the observed results.
This is all much easier to think about if you consider current through the resistor, and treat the diode as an unknown.
Anyway, in the end I think we're saying the same thing, that it's the leakage, not Vf per se that is the issue, although a higher Vf could result in a higher leakage, so they're related. And yes, if they're really being driven at 20uA (155-135), wow. Yeah, maybe there's 10uA of leakage current in the diode. It seems to me that's maybe just driving them too low. If the mcu has 135uA of leakage anyway, just double it and aim for 260 total. Then there's probably no problem. A factor of 3 off in led current will still work then.