In the former case, though, it could be argued that the more literal "Sam's idiocy" also technically works, and that "Sam, you're an idiot!" is simply a typical case of recognizing that "Sam's idiocy" is not something someone would ever say in English.
Deep analysis of の when used in this sort of grammatical capacity (as a so-called particle) will always take you back to the possessive. The main point is, you shouldn't think of it purely in terms of equaling an apostrophy-s even if that does seem like the simplest approach, because eventually you will be doing more complicated mental gymnastics to understand it that way, not to mention to translate it.
Also, I think "Sam's idiocy!" is maybe going down the wrong path for that particular pattern. The noun following の pretty much always feels concrete ("idiot") not conceptual ("idiocy"). For example, how else could it be the subject of the sentence "Sam the idiot/That idiot Sam forgot his umbrella." (サムのバカが傘を忘れた。）? Saying that my idiocy forgot the umbrella doesn't really work, does it? The person saying it certainly isn't talking about my idiocy, per se. He's talking about me.
As another example, to pick on a childhood friend of mine, ピーターのやつ or ピーターのやろう means "That guy Peter" or even "That bastard Peter". Again, it's quite the contortion to put it into "Peter's bastardliness", right? Especially if it's going to be the subject of a sentence, right?
One way to think about this might be that it's adding a degree of clarity to the statements あのバカ or あのやろう - that idiot and that guy, respectively.
As a final example of の's flexibility, if you put the name on the end, you can do things like 料理人のマーク (Mark the chef) or 大工のジャック (Jack the carpenter), too.
In the end, while you
can force yourself to interpret these through apostrophe-s, I don't know why you would want to. It's best to understand what "possessive" means in general, then take の as its own thing, IMHO.
