It was on United and I was mostly *S back then. I believe anyone can have a free "upgrade" to E+ by asking a gate agent with some status on boarding pass (at least on united). I am just guessing here but I think that on a GA's screen, E+ and E are basically the same. It is probably considered by the system as the same class of travel, thus not an upgrade per say. Plus, it is a standard benefit for UA frequent flyers so I guess many agents are just not familiar with which privileges are also offered to *S and *G from other airlines.

Regarding "real" upgrades to business indeed I think that these are so rare that it might be hard to find a pattern by airline as sdsearch mentionned. Maybe some specific cases (i.e if you fly from LIR on UA, and get the same checkin agent as I had, ask for an upgrade because that one specific agent probably does not knows the rules well enough), but I really doubt you can find any pattern since it is really really rare and there most certainly is no correlation between those rare cases