Sure it matters which schools you come from. Anyone who says/thinks the competition is irrelevant is in complete denial. Just look at the admissions stats for undergrads to get a good feel of where the average is at. The average is very important to determine where in the curve you will fall, so better not find yourself in a room full of 1350+/1600 SAT kids.
I looked at all 5 years on predents (for lack of a bigger,better, accurate source- maybe doc has something?) and queried two sets of data: AA<=19, Sci GPA >=3.8 and AA>=21, Sci GPA <=3.3
Note: I only looked up California for state residence (and blanks) to identify UC students. This does not imply that other schools do not have a similar or an even more skewed distribution or that there were no OOS students at the UC schools (just impossible to locate)
Out of 122 results for Sci GPA >=3.8 and AA <=19, I found: 1-UCR (3.9/19), 1-UCI (3.83/19), 1-UCLA (3.84/19), 1-UCSD (3.8/18). This represents 3.3% of the "high GPA/ low DAT" group.
Out of 270 results for SciGPA<=3.3 and AA >=21, I found:: 2-UCR (3.07/22 average), 4-UCSB (3.25/21.5 average), 14-UCLA (3.07/21.43 average), 7-UCD (3.02/21.86 average), 9-UCB (2.99/ 22.44 average), 7-UCI (3.05/22.14 average), 3-UCSD (2.77/ 22 average). This represents 17% of the entire "low GPA/ high DAT" group.
A cursory look into Sci GPA<=3.3 and AA <=18 ("low GPA/ low DAT") group shows only 2 UCB entries out of 300: an Environmental Earth Studies major(2.99/17) and a Anthropology major (3.08/17). There were more from the other UC schools in this group as well.
I may have missed a few in there but not enough to change the averages by much. There was a single CSUs, SDSU, Cal Poly SLO, UOP here and there. Anyone interested in finding their school's representation in these two groups, be my guest.