Hi,
I live in Brighton--we just moved here over the summer, so I just went through the process of enrolling my kids in the school district. We had to show a lot of proof that we really lived here--deed to the house, etc.--and as far as I know that's the rule--you have to live within the boundaries of the Town of Brighton to send your kids to school in the district. I don't know how it is for other towns but I suspect it's the same. It would have been huge news if kids from the Rochester City School District were suddenly allowed to enroll in other districts.
I did see something online about some Rochester schools being involved in something called the "America's Choice" program--maybe that's what you heard about? But I can't find anything else to tell me which Rochester schools might be participating. Here's their Web site:
http://www.americaschoice.org/
I think your best bet is to get on the phone in the morning and try to get some answers from the people at your child's current school. Surely they can tell you--although it seems to me that if they gave you a list of schools to choose from, those are going to be the ones you have to use.
Sorry I couldn't be of more help!