I think the issue in telling someone to rely on technique rather than their strength, is in working to develop a higher quality in the technique. If technique quality is poor, you can still make it work if you put a lot of muscle into it. If technique quality is high it is more efficient and can be more effective even with less effort and less muscling of it. So when training, you want a student (and yourself) to focus on quality of technique, for better efficiency and better effect, with less effort.
But that is not meant as an indictment of strength or stamina or speed or whatever natural and athletic attributes one might have. When facing a real opponent, whether in the ring or on the street, in the chaos of combat, quality will diminish. Now is when athleticism becomes important, when the conflict is real.
So, of course athleticism in all of its parts is important. It goes together with technique, but it is important to give appropriate attention to technical development in order for optimal use of that athleticism.