One thing to note is that you can easily justify that the fact that even if they put the armour on, they can't use it remotely effectively. 

Armour is not just a magic shield around you. You need to know how to move to take hits on the strong sections, and how to guard the chinks and joints where an opponent could land a lethal blow. A druid who "would not wear armour" would not be able to do this.

It would be perfectly acceptable to give them an AC *penalty* instead of a bonus (because they won't be able to use their natural defence skills effectively any more), *and* to diminish their connection with nature (disadvantage on all druid-related behaviour), thus negating any benefit to the armour and applying a penalty.

If they refer you to the strict rules, then they lose the argument because the rules say they won't wear the armour. If they don't, then the armour is useless to them, which is canonically accurate.

Edit: It's important to note that 5e, by design, puts a lot more power in the DM's hands than its predecessors. 3.5e tried to cover every eventuality via the rules, which was very comprehensive and detailed, but arguably led to a culture of rules lawyering and a major accessibility problem. 4e was also restrictive, trying to keep everything simple, which led to a more "board/video gamey" style. 5e is different. When they leave something open it's because you are *intended* to choose an option that fits your gaming group rather than being forced to kill a good story because of an arbitrary ruling in an expansion book. This is one of those occasions.