Wombat – I think you slightly misunderstood what I’d said, re jazz and improvisation (or I wasn’t as clear as I should have been) but otherwise I don’t think we’re in particular disagreement. As for Peter disagreeing and then vanishing, I think eilam and you were hallucinating, as I made such great sense it’s unlikely anyone could have posted a truly opposing viewpoint. 
I play, and have played, lead guitar most of my life, before flute and ITM, most of which is/was improvisational, rock, not jazz, but the idea’s the same. The key difference between an improvised solo, in rock, jazz, etc., and improvisation in ITM is that I am (on guitar) creating melodies around a chord or bass structure, and I’m not (during the improvised solo) limited to the melodic or rhythmic confines of any particular tune. I’m not reinventing the wheel there, either, in terms of scales and patterns, but I am creating melodic passages that will (most likely) not be heard the next time I solo, or ever again. I am not playing a variation of a tune, or an embellishment – I do that during a song, of course, diddling like Hendrix on and between chords, but that is not real improvisation. That’s embellishing, being fancy, etc. It’s a skill, it takes taste and timing to do it right, on-the-fly, et al, but it’s not really improvising. It’s just having fun with the structure.
In Irish music, the added triplet, chordal pattern, what have you, has to be worked into a given tune and remain true to the tune in order to return to it, like a singer adding personal touches to a well-known song. What Mary seems concerned about was the embellishments, and the learned variations that come and go and alter the tune briefly, but are still within the tune itself. I feel (and the missing Peter may disagree) that this is not true improvisation. We can all split hairs as to whether an “improvised” note, triplet, rhythmic stutter, etc. are, in fact, improvisations or just variations, or simply playing loose and having fun with a melody. All this (I have no argument) is done in ITM, and some more imaginatively than others.
My main point, to her, was not to worry so much about this. Knowing the tune very well and being flexible with its many possible interpretations is more important than going off on new variations and embellishments. Well-versed ITM players know how to embellish a tune because they know the tune inside and out and they know what variations and embellishments will work. They are doing what comes naturally to a standard tune, in their own personal way, after learning a ton of other such tunes.
If what I’ve said was interpreted to mean that I believe that there’s no ideas or creativity done “on-the-fly”, I was then not clear: Of course there is. But the patterns and variations are not improvisational wizardry, they’re tried and true embellishments, learned passages, mixed and matched, and – this is the part that good players do best – all are done with creative and tasteful discretion. An embellishment or variation can be as simple as leaving out a note or two in the right spot, not just adding stuff. Knowing how or when to do that best is both creative and (often) inspired, and generally unplanned and off the cuff.
All arguments, of course, are valid. You may disagree, and then disappear.

Gordon