The semantics difference between the phraseology of "track direct..." and "recleared amended route.." were, as I stated above, negligible difference.
However, I also understand that the "amended route clearances" that were issued were actually issued as route designators (e.g. W636) rather than "recleared amended route SGT planned route" - hence the difference, as in an audio replay it doesn't sound like the aircraft are off a route and also therefore not tracking "direct" to a point (very important re: the management directive) - it just so happened that the new "amended" route coincided with the direct tracking that was requested.
I guess to argue a point if you have them on a published route it makes a difference in a radar fail scenario where there are far more likely to be published lateral separation diagrams than for arbitrary lines across the screen where the only quick way to establish separation is using levels.
Like I say, though, I think those issuing these "amended clearances" will still need to justtify such actions should anything untoward occur....