Good god; there is a suggestion, in that last statement, that a pilot should use a modicum of common sense: or not to be trusted, hence the instruction.
There are grey areas. In my then airline, at home base, >3000m TORA, B757 on a 3 hour trip so about half full load, RTOW tables no computers. Runway contaminated as MED/POOR, MED, POOR. SOP = no ops if POOR runway surface. You could certainly be airborne before the POOR, but where exactly would you be at V1 and where would you STOP. Some said do a balanced field calculation using MED and see what you need. If it is <2/3 TORA then you can go. Captain said No. Night flight, all offices closed. Airport said they had no plans to re-clean the POOR. They had done all they could and achieved no improvement, especially as temp was falling.
Some said do a landing performance using MED at TOW and if that was <2/3 LDA then go. Captain said No.
Quite simply it was a grey area. Later, a B747 freighter landed, having calculated, we assume, that they could stop in 2/3 LDA. They didn't and ended up nose wheel just on the grass.
Captain had got home by then. Who's to say right or wrong in a grey area.