The AOs do know that there are differences between public and private schools.
I know in my parent interview at one school, the AO commented that the SSAT scores are viewed differently depending on where the applicant went to school. So, for example, a 70th percentile math score would not be a red flag for a public school high honors (all A+) student taking the highest level courses their school offered, but would be a red flag for a student from a place like Belmont Day School, where students have SSAT prep, etc.
I would suspect that the same is the case for teacher rec’s. If you’re coming from a public school that’s Title 1 and/or in an area where independent schools are a foreign/exotic concept, this may be taken into account. Especially this year, where letters are likely to be… terse.
One thing I would suggest is to take advantage of the option of a supplemental letter of rec. , someone who knows you well enough to say something meaningful. This can be school teacher, a private teacher, a coach, a GSUSA or BSA leader, or even, depending on the school and your faith tradition, a religious educator - basically, anyone who knows you well that can highlight aspects that you want to emphasize.
If you’ve been dancing for 10 years… hit up your dance teacher.
If you’ve been 1st chair in the orchestra… hit up the orchestra teacher.
It does not matter that you are not interested in becoming a professional dancer or musician. It does matter that someone can say you’re a 3 dimensional person that they like having around. You don’t have to be a soloist - schools need team players and leaders too.