I'm sure that someone somewhere in some game at some point someone has had their PC put on metal armor to sneak into a castle. But there are sooo many issues with that hypothetical. Like ... does the 8 strength wizard put on full plate? Guess you aren't using the variant encumbrance rules. Hope nobody notices the dwarf in a castle run by orcs. That fighter with the +1 plate is going to swap out for the chain mail that's standard for the guard, right?
When I've run across similar scenarios, someone polymorphed, did an illusion of some kind, hid in a bag of holding, pretended to be a prisoner, climbed a rope the others threw down, or one of a hundred other ways of dealing with it.
This scenario will never happen in any game I ever run and over decades of running and playing games with more DMs and players than I can count I've never seen it. But it still doesn't matter. The DM not giving you an option? Like I said before, they're being a **** DM. It's their game they can make something else work. Even then, we know that according to the rules a Druid will be unwilling to wear metal armor.
But let's say the druid ignores the clearly stated rule is willing to wear the armor in this one oddball niche scenario and the DM allows it. So what? That doesn't mean he will wear armor any time else. Sneaking into a castle does not justify wearing the armor at other times. A vegetarian will not eat meat ... but if he's starving to death and there's no other option they may make an exception. But if he continues to chow down on burgers after other options are available they're no longer a vegetarian.
Like I've said before, I wouldn't allow it because in all but a couple of cases I follow the rules. I don't see a justification for it, if someone playing a druid wants better armor we'll work on an alternative. I wouldn't have a metal armor wearing druid in my game any more than I'd have a 7 ft tall halfling. If someone tells me I'm not the boss of them and I can't enforce the rules of the game I will let them know that not only am I not their boss, I am not their DM.