What's in a Key?

At the Irish session last night, Ernest made a comment about how he doesn't really think that Irish tunes have keys. That made no sense at all to me, so of course I asked him to explain. He pointed out that a lot of this music developed as pure melody, without a harmonic context, which may be true, but I don't think that prevents it from being in a key. Plenty of tunes are full of arpeggios, so there is some harmonic context, even if the chord progressions don't always match up with classical music theory. Most importantly to me though is the tonality. There are some weird tunes out there, sure, but with most of them, it's easy to tell which note everything wants to resolve to. Ernest also cited examples of old recordings that have chordal accompaniment, but that use unusual chords that wouldn't seem natural in the context of a particular key. I'd have to hear an example of that though, and figure out precisely what chords were being played, in order to decide if I think that affects it. But my guess would be no. You're allowed to do unusual stuff with chords without forfeiting your key. But it made me wonder about what the most minimal, precise definition of "key" would be. For myself, I think I'd say forget about chords -- there just has to be one definite note where the melody feels resolved. The other notes can vary. I'd count "D modal" as a key, for instance, without needing to choose between D major and D minor. The point is that it all revolves around the D (or whatever note). Anybody else have any thoughts on this?