It is true that there's a lot of variability in grad schools, but it's like undergrad in that regard. Yeah, sure, you can get into a program with mediocre stats, but that's not the same as getting into a good program. It's also not like med school where even if you go to a bottom tier school you'll still become a doctor assuming you don't screw up. Where you go to grad school/who you study under has a big impact on how your career will turn out. To see what I mean take a look at any science department's faculty. You should notice a pattern about the type of schools they got their degrees from.
The PI has to pay the grad student's stipend and tuition. That's not cheap. PIs also have a vested interest in trying to get the best grad students they can since an incompetent grad student is liable to slow down the lab's progress, force replications of repeatedly failed experiments, and in a worst case scenario cost the lab grants. Meanwhile a talented grad student can do the opposite.
Most grad school applications don't even have a spot to list ECs on. They simply do not care. Applying to grad school is more like applying to a job, no one cares that you volunteered for four years at a homeless shelter or built schools in Africa because it has zero relevance to how good you'll be in the lab. For the same reason, no one cares about what someone unrelated to your chosen field has to say about you, and what a professor has to say about your performance in a class isn't nearly as valuable as what a PI has to say about your performance in a lab. Again, most of your time spent in grad school is under one PI. While med school adcoms may be notoriously unconcerned with the admissions process, grad school adcoms tend to be a bit more interested seeing as how they may very well be stuck with one of the people they admit for the next 5-7 years.