Is this generally true? If so, how to find those scarce sources of them?
Depending on what program you are looking into, the universities (at least in the US) should have grants and fellowships predominantly based on merit. (Some grants may be issued by the university based on proven financial need, but it is often not much and there does need to be a need). Your best option is to see what fellowships are offered by the university and apply early on, as most deadlines for the fall are early January.