Nah, the wealthy parents end up leaving Boston because the lottery is fairly nepotism proof. The BPS lottery is frankly too complicated and confusing to be easily gamed -- I don't even think the people running it even understand how it works. If it were that easy to game, the rich parents would have had it locked up decades ago.

There was a huge dust-up recently about exam school seats, because they changed the rules to give seats to a more geographically diverse set of students. This resulted in a lot of angry upper-class parents, because (surprise surprise) those upper-class neighborhoods had previously been overrepresented in exam school admissions.