i have also been wondering about away rotations and talked to 4th years, residents, and faculty at my program. here's the summary of what they said:
if you are a "strong applicant" (research, good step 1, interesting extracurriculars, etc...) an away rotation is just as likely to hurt you as it is to help you. you're likely to get interviews most places regardless, so you don't need an away to help with that. all you might do is find that one random resident/faculty who you won't click with and make a bad impression, potentially costing you a spot on their list. however, if you're a less ideal applicant (low step 1, etc...) you might raise your chances of interviewing and matching at that program by showing them what a rockstar you are on an away.
aways will only help you at that program. no one else cares where you rotated (so rotating at brigham doesn't make you more competitive because its a competitive program). the only exception to this is if you get a great letter from someone at that program who is well known, but that applies to your home school too.
i was also repeated told to do aways to figure out if i wanted to go to that program, not to try and guarantee a spot.
all this being said, i was told if i had my heart set on one program i should try and rotate there as it may help my chances.
in regards to all the mixed opinions out there, i'd attribute it all to differences between programs. some might like to take those who rotate there, others don't care. just like some put a lot of weight on LORs and others don't.
hope this helps 🙂