Interesting question,
Groin. Actually, the points you brought up made me think about an additional question. If dragon flame could consume rings of power but not dwarven armour, then is the dwarven mail actually stronger (or rather, more endurant) than a ring of power?
I don't know about magic, though - I'd rather talk about power. The dragons were, after all, beings of a different time, a time when everything was greater, fairer, and younger. I find it perfectly reasonable to think that beings as mighty as the dragons would be able to destroy rings of power. It's the comparison to the dwarven mail thingy that feels problematic.
By the way - the passage "but there is not now any dragon left on earth in which the old fire is hot enough" somehow makes me awfully sad.
Sorry,
Groin - instead of answering your question I just made another.
What is this, answering a question with a question? Brings me in mind of Rosencranz and Guildenstern...