Proud Tatty, Chazal are just as mechuyav in the mitzva of Lo Saamod as the rest of us. Pshat in the Harugei Malchus was whether they should daven to annul the decree.
Also, the gemara discusses medical cures of their times in many places, so the idea that they had no interest does not seem to be correct.
Furthermore, I believe the Vilna Gaon said that he did not study medicine, because then he would have been obligated to treat people all the time, and he wanted to learn instead. Reb Moshe also has a tshuva that one is not obligated to study medicine, but if he knows it, he is obligated to be matzil nefashos. (If I recall correctly.)
Finally, the gemara in Sanhedrin says that Rav spent 18 months on a farm to learn the difference between a mum kavua and a mum oveir. Why did he not learn this in the beis medrash instead?