Short answer, yes. You can rent in a public school district and she will be eligible like every child in the catchment area provided she lives there.
But I’d like to follow up with a few thoughts and questions.
First, what specifically would qualify as a “competitive” high school? Does it have to have an IB program?
Second, have you considered the inverse relationship between opportunities to lead and come out on top, and the stats and scores of the school (i.e. top schools will have tons of high achievers and fewer opportunities to lead)?
Third, have you considered how your sister may feel going to an ultra-elite public with very privileged families, since most of these top competitive schools are in areas where the median income is around $150-$200k annually?
https://www.nytimes.com/interactive/2016/04/29/upshot/money-race-and-success-how-your-school-district-compares.html
Fourth, most of these statistics on top schools come from % passing a state test. How rigorous is the state test? There’s no national standard. So you will find more higher ranked schools in two situations: one in which the state has a lower bar, and one in which the state allows for “cherry picking” in public charters, i.e. you have to gain private admission to a school through tests and local residence is not enough. For example, in Boston, charter schools are very big and you may not get into them.
Take a look here to find out where public schools are actually performing.
https://www.nationsreportcard.gov/profiles/stateprofile
Massachusetts does well. California and Texas, not so much. California has a few top schools but they also have lower standards and rank behind Wyoming… every time. The reason you see this difference is that the scores for pass rates are based on state benchmarks. There is no national benchmark. Even though California and Texas have more elite schools than my state, they come out below Washington and New Jersey in national benchmark exams.
You can easily use Great Schools or Niche to find top-ranked schools. Or just use the US News and World Report ranking. But the education your sister gets will not depend on how many other kids have access to what they need to pass a state test. It depends on how well she fits into the school.
I suggest finding an area with a large community with a similar background and a solid public with an IB program–don’t worry about the ranking, worry about whether people talk about the community there. That’s where she’ll have a chance to really develop her leadership skills and dive into her passions while growing as a person.