Welcome to the forums.
Your prehealth committee is right that unpaid tutoring can be considered non-clinical volunteering. That said, practically every prehealth/premed has tutoring/teaching/mentoring experience that it won't make you stand out or help you in the process as much as service orientation activities will (200 hours soup kitchen). The issue is value for an admissions decision, not whether they are non-clinical volunteering. TL/DR: Both opinions are true.
Additionally, tutoring/teaching/TA is a separate category in AMCAS last time I checked.
You should get 250 hours before submission to keep pace with your peers. As we mentioned above, many of your peers in the high-metrics pool will have hundreds to thousands more than you.
I also would like to see more exposure outside of the OR, such as non-emergent primary care. Your 200 hours is okay, but in a contest among high-metrics applicants, does your prehealth team think you have enough? You attend an Ivy program, so shouldn't you have just a bit more (your 260 clinical hours with shadowing is less than your 350 non-clinical experience hours and "other" 450 experience hours). It probably won't screen you out, but I'm curious.