Hi!
I didn't read the whole thread that Randall linked, (I read what Mr Mele had posted about the class though) and I don't see what is so funny about it.
For me personally it is too much about defining what constitutes a "single art" that anything conclusive could be said. Same weapon, same period, at least up to a point same context and a few similar basic aspects like trying to hit your opponent in the head and stay safe - yeah, sounds similar. Then there is the question whether the treatises represent a full and complete picture of what the masters were doing, to which the answer is that we can't know for sure.
I don't think Fiore enthusiasts collectively maintain that Fiore's art is completely different from other traditions (who is saying that? I'd like to try and set them straight!

), but in my opinion it is also different. But please understand that this is partly due to how I see the meaning of something being 'different'.
To me, Fiore's breaking of thrust is not Liechtenauer's Krumphau, for the following reasons:
Context: Fiore does the technique against a thrust specifically, L. does it in various places
Ending position: F. ends in his porta di ferro, preferring to step on the opponent's blade, L. goes into schrankhut
Followup: F. strikes a sideways false edge blow, L. a downwards one (or so I've been taught, if you have other interpretations, that's OK since they are unlikely to be closer to the Fiore version!)
Hand position: F. is using a more 'normal' cutting angle, supporting the blade edge aligned with the forearm, the L. works best as more sideways action, with the thumb supporting the flat of the sword allowing for a different way of moving the sword around
Footwork: F. seems to work best doing the accressere+passare combination towards the attack (in order to get the stoimp on the blade this seems to be the only good alternative!), L. works best stepping away from the attack.
I simply choose to see the differences instead of focusing on the similarities and categorizing the two actions under an umbrella term of my own invention - surely there is nothing wrong with doing that?
Now it might be that both actions originate from the same root (from where the mutacio gladii might be coming from as well!) but the different masters refined the techniques to two ways of expressing the same idea, better fitting their overall way of using the weapon. Now, given the completeness of their written and illustrated legacy, I think that the masters' works can be viewed individually and different systems can be seen; different - but not by any means radically so.
To me, in the process of interpreting material that is as difficult to access as these 600 year old sword arts, doing this sort of analysis on the specifics of one masters' techniques compared to others is extremely valuable.
I hope this clarifies my position! I don't mind people speculating about there being only one art, but I'd like to see it better defined what they mean by that. Clearly what was done with a rapier was very different from what was done with a pollaxe in armor - but both activities still shared some basic components: cuts, thrusts, parries and the need to give and not receive. What is the problem of looking at sources in isolation as well as part of a larger scale?
And by the way, I don't really agree with Greg's post on the other forum. The class they are running will probably be a lot of fun, but perhaps it'd be better without the agenda suggested by the title, of showing that there was just one art.
Yours,
Ilkka