The writing on that website is not very well clear. LACsm are ‘private’ colleges, meaning that the government does not provide any direct funding the way that they do ‘public’ colleges & universities. For domestic students that means that their in-state public university is typically the least expensive option (there are a small number of public universities that have a few big scholarships, which are extremely competitive and a couple who give big scholarships for high test scores).
But private colleges have more discretion on financial aid- whether “need” based or “merit” aid. For international students, who don’t have a ‘home’ state this opens up more possibilities for funding support. The ‘popular’ state universities (for example, UC Berkeley) are now more expensive for out of state (OOS) students than many LACs. For students with the stats for UCB there can be financial or merit aid at LACs.
Two things to remember about aid:
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‘Need’ based aid is based on the school’s calculation of your need, not yours.
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‘Merit’ aid is basically a quid pro quo system, which is usually a ‘you have high stats that improve our average so we give you a discount to come’ calculation, so it will usually come from a school that you are v v well qualified for (many of the top LACs do not give ‘merit’ aid at all, only need based), OR it has inflated prices and gives lots of students some ‘merit’ aid, as an incentive.