I don't know if you're fully understanding me. At least in my program, if an applicant gets to the point where GRE is being used as a tie-breaker, there's not really any question as to their aptitude, personality traits, or that they have the credentials to back it up. This means that they have substantial research experience, though not necessarily any publications. I didn't have any when I was admitted last year and I received multiple offers from fully-funded programs. Furthermore, an applicant can have an absolutely stellar research CV and really undercut their chances, because of their behavior and demeanor during interviews. I've seen multiple applicants tank it, while other applicants with less substantial research productivity get offers, because they had a better fit with their prospective labs and just generally seem like better choices for someone with whom you will spend the better part of a decade.
This is not to say that the applicants who didn't make it to the tie-breaker stage are necessarily not hardworking or wouldn't make great psychologists. It's just that you really can't blame faculty for not selecting these people. There is a very limited supply of spots and they can't really risk them on unknown quantities in the forms of people who don't have the requisite academic, research, and clinical credentials to demonstrate their aptitude. There might not be any research specifically backing this up, but faculty have been through grad school and they've seen what it takes to make it through and select accordingly.
Again, I'm not sure you're really understanding my perspective. Fellowships are often on the university level, not the program level. This means you are not simply competing with other clinical students for them. At least at my university, your competition is every other doctoral student in every program in every department in the entire university. These disparate programs and their respective fields have different standards, expectations, norms, etc. This is to the point where it's difficult, at best, to compare them like we would compare between students applying for the same clinical program. In some fields, it's far more common for people to have publications before beginning their doctoral programs, while in others it's far more common to have a terminal master's degree from another program first (e.g., counseling, social work). Thus, comparing undergrad GREs and GPAs is quite likely the fairest way of comparing students across disciplines.