Isn't this more like a cocked/leaning die, or the die falling off the table? In my experience do overs are generally used for malfunctions. I mean, we'd call a do over for the wiffleball going into that darn tree again, but probably not when Jack's hit scores four runs.
Well, I think a hardcore wiffleball player would say, "You knew the tree was there, and if you couldn't keep out of it that's your own darned fault, now isn't it?"
Without extenuating circumstances (like, say, Carlos was busy talking to the cute girl in the next yard when Jack scored the runs) nobody would call a do-over then, no. But that's because nobody could say it was lame.
But, here's where the analogy breaks down: in wiffleball, there are two sides, in competition, and they are playing the same functional roles in the game. In an RPG, the two roles (player and GM) are not functionally the same, and the two sides are not competing with each other.
If the games are structured differently, how lameness is to be determined is also likely to be different. In an RPG, we may all accept that the GM is in a good place to determine what's lame.
In golf, you wouldn't call a do over for a hole in one, right? If someone hits a hole at par +10, is anyone going to say, "Just write down par +2." Right?
Not in a competitive tournament, no. But, say, in mini-golf, there is apparently a long and wide tradition of writing down par (or sometimes I've seen 5) no matter how far over par you actually go. You wont see "do over" yelled at the high-school softball game, but you will in backyard wiffleball.
Thus, sometimes altering the game is allowed, sometimes it isn't. Context matters.
Need another example? Contemporary videogames! Once the business need to keep sucking quarters out of players was removed, save points and unlimited resurrection became pretty much standard operating procedure. Unlimited do-overs! Again, a different way to determine lameness, because the game structure is different.
The point is that even very young, we clearly have the idea that the actual literal events may well not stand, that the vicissitudes of chance are not necessarily what we'll take as the most fun all the time. You asked for examples when not adhering strictly to events was seen as okay. I think I've given several already.