I have to say that AreOut has, for the very first time in more than 20 years contributing to this site, made me consider blocking a poster.
To be more constructive, a quick Google suggests this is not the first time something similar has happened. I have no idea if the same systems were used for performance calculations but perhaps there is an easily missed HF gotcha.
More generally on the ATC/pilot responsibilities, as an ex-controller myself, I concur with pretty much all explanations to suggestions that ATC made an error. Listening to the recording it sounds like the controller did a pretty good job in, perhaps, difficult circumstances. Applying European ATC procedures there was little more that the controller could have done in the circumstances (that is to say, it was not inevitable that the TORA would be inadequate, and I have seen lightly-laden jets get off in remarkably short distances).
There are so many variables that contribute to take-off performance calculations, the only people who will really know the runway length required will be sitting at the front of the aircraft. The principle generally applied is that pilots fly the aircraft and controllers stop them banging into each other - crossing that boundary should be limited to suggestions only and these will rarely be necessary. The UK introduced a procedure a few years back whereby ATC was supposed to warn a pilot if they were about to start an approach below minimum (for AreOut's benefit, approach minima are another thing that are affected by many factors and are the pilots' responsibility to calculate) - it was a complete shambles and, IIRC, the CAA guy who designed the procedure was ripped to shreds in court when the CAA tried to prosecute a pilot for landing below minimum.