Look at Washington and Lee - Lexington is more rural than Carlisle.
Here's the catch: Washington & Lee has a moderate amount of prestige NOW. Dickinson does not, and is attempting to purchase prestige. Your analogy only works if you can find a low T2 law school that spent TONS of money in recent years and became T1.
Cardozo is an example of a fairly new law school that has spent considerable effort in terms of recruitment of faculty and students. The faculty is by all accounts very well regarded, but the school has yet to crack T1.
My own Temple University constructed a new building that opened in 2002, completed extensive renovations in its primary building in 2005, hired new faculty and increased its endowment 10x in the space of a few years. This has not changed its ranking. Temple still floats in between the high 50's to mid 60's.
Money can buy new buildings and new academics. What it cannot buy is decades of brand-name prestige. The deans, lawyers, and judges who fill out USNWR surveys can't possibly keep track of all the new buildings and faculty hires that law schools make. They will judge schools based on the alumni they know and their preconceptions (whether right or wrong) about the school.