When you use the ring of rings you aren't preventing the wounds, you are taking burdens instead. That's why you can choose to wound him twice if exhausted when wearing that ring (you still take two wounds, but the ring changes them to burdens), but if you prevent either of the wounds (armor, sapling, etc) then Boromir has to take 3 burdens as per his text.
I'm afraid you are confusing two different types of effects here (with two different templates).
1. Do [action1] or [action2].
2. Do [action1], [player] may [action2] to prevent it.
The first group of effects has the following rules in Comprehensive Rules:
"If the effect of a card or special ability requires you to choose one of two different actions, you must choose an action that you are
fully capable of performing (if possible)."
The second group of effects has the following rules in Comprehensive Rules:
"If something happens to prevent one effect which in turn
would have prevented a second effect, the second effect is performed."
Boromir, Bearer of Council belongs to the first group, so the clause about prevention does not apply to him. So if you choose to wound Boromir (and you're "fully capable of performing it"), and you prevent the wounds (for example with
Sapling of the White Tree), you
DO NOT add burdens. You would have to add burdens, if text of the Boromir was following the second template - so... "At the start of skirmish involving him, add 3 burdens, you may wound him twice to prevent it".
And I still think you can't choose to wound exhausted Boromir twice as you resolve his trigger, because you're not "fully capable of performing" it, that is (without help from other cards) to physically put 2 wounds on him (he'll die after receiving the first one). Even if you have a card that allows you to prevent it (or do something instead), I think you should not be able to choose that possibility, because if it was allowed, there would be no clear distinction of what is possible, and what is not.
Lets imagine you have two event cards in hand with text - "
Stealth Response: Remove
![Gondor [Gondor]](https://lotrtcgdb.com/forums/Smileys/classic/gondor.png)
token from your
![Gondor [Gondor]](https://lotrtcgdb.com/forums/Smileys/classic/gondor.png)
condition to prevent a wound." You might argue - "because I have these cards in hand, I can choose to wound Boromir twice". Then your opponent would have to show you his
Relentless card in hand and say - "No, you wouldn't be able to fully perform the action, so you can't choose it" - all this without even playing a single card or effect.
I think a distinction whether you are "fully capable of performing" an action should not take into account any cards or effects (or possible actions), except ones already in effect, which are preventing you from doing something, like: "[classifier] cannot take wounds", "[classifier] cannot exert", etc. If you allow any advocating of "I can choose that, because I can play this card and then this card, followed by this effect" we'll be in trouble (not to mention it's impossible to implement this on a computer, as when figuring out, whether you can do something, it would have to follow all possible lines of play).
The only thing you could argue here, is the part, of whether you should be allowed to wound characters as many times as you wish, or is this choice limited by vitality. I'm not decided yet on this, but if we decide to go this way, it has a following consequence (probably one of many) - it's allowed to choose to wound companions with 0 vitality which are still in play.