If you get a chance, I'd be interested in more specific information about what their regrets were and why they would do things differently (Tier 1 public HS vs Tier 2 private). It sounds like the private worked reasonably for them, from this info, but there must be something that they thought wasn't ideal? Expense or something less obvious?
Not that a Tier 1 public HS is an option in my locale anyway (insert eyeroll icon), but we debate public vs private often.
Their son was reading at a 6th grade level at 5 and doing multiplication/division. They bought the Public School "best K in DFW" koolaid, put him in public K, until they looked at the curriculum. They tried to get a skip or some other differentiation and got no where.
They pulled him out and put him in a private K-4 school in K at 5 where he got to do self-study.
They were very happy with the private school he went to.
A few years ago, they learned that public school in TX has to take a kid into the grade they are in who has completed grade 2 or higher at an accredited private and who is six or older. In other words, if a kid has finished 4th grade and is 7 then the publics have to take him into 5th at that age.
I've spent some time looking at instructor bios since that discussion, too as the teachers are the ceiling.
I looked for real credentials in the specific areas of instruction. Most instructors have MS in Education or a BA and teach math. I am sure they can regurgitate the book, but a PG kid will run into a wall with the MS/BA in Ed.
A PHD or MS in Math can take them a lot further and will know where they are ignorant and find the kid some better help.
I have no idea what you mean when you say "Tier 1".
By Tier 1, I mean highest number of NMSF on a percentage basis for the Senior class at the HS for that school (if private) or district in a given metropolitan MSA. Generally, >5% of the class or at least 20 NMSFs per year.
The top privates in the DFW area regularly get > 20% and the top publics see 30+ NMSFs in their high schools.
At such a "Tier 1" school, a PG kid should find friends in every class.
