I agree, I worked that out on NYE.
So to summarize: the reaction of iron in the presence of water and O2 is spontaneous, yes.
In the presence of hydroxide, there is no O2 to react with so no reaction occurs, which explains the lack of corrosion seen in the earlier lab the question references.
I understand all of that just fine now, but I will have to email my teacher as I don't understand why the question states the reaction is spontaneous.
In answer to my original question of explaining the non-reaction with the provided half-reaction, could it be that the concentration of OH-(aq) is much higher than the concentration of O2(g), thus no O2(g) is present to react with the iron nail?