OTB:
“Why do Chazal tell us to believe it? Who cares?”
So that we won’t automatically dismiss anything the goyim come up (especially regarding practical sciences such as physics, biology, chemistry, etc).
“How exactly do you learn Chochma ‘second-hand’?”
I’m not sure exactly what you mean by that, but you seem to be misreading my diyuk. What I was trying to point out is that the reason the Taana phrased the Mishna “if somebody tells you that there is chochma by the goyim, believe them” instead of just saying “there is chochma by the goyim” is because the only way one should be hearing about the goyim’s chochma is from somebody else; he should not be looking into it himself.
“Are you telling me the Rambam learnt his medical knowledge second-hand with no non-Jewish sources?”
Actually, I heard a very interesting speech which explained that the Rambam learnt medicine to become the top doctor in Eypgt in order to gain political power, which he used to preserve Torah-true Judaism that was under attack by reform movements.
Also, the Chovos Halevavos and the Rambam had to go through goyish philosophy in order to disprove any parts that were against Jewish philosophy.