Sloppy joe, you speculate. Before starting to apportion blame ( e.g. the MS pilot) I would like to hear the instruction he got and the read back he gave ( if any). As to crossing stop bars, ( if that was a factor here ) this is another important issue as in too many airports you are still cleared to cross/disregarding red stop bars.
Bad phraseology still kills people today. Training on it is without stress, and we all know that when stress jumps in , as you correctly say, people do very different things. You will notice that on the tape shown the controller did not use any call sign , I suspect the LH saw the intruder and did not question the order. Luckily it was daylight CAVOK. At night or IMC , a few extremely important seconds could/ might have been lost by PF/PNF questions or even a read back " was that for us LH 211 ? " and we would have a very different discussion now.
Never underestimate phraseology.