it's not an advantage in "headcount" sports, which based on one page I found are:

Football (DI FBS only), Basketball (DI men’s and women’s), Tennis (DI women only), Gymnastics (DI women only) and Volleyball (DI women only).

In those sports, an athlete "counts" if they get any scholarship money, from $1 up to full COA...so you don't see partial scholarships and you can't give an academic scholarship to "save" an athletic one. These students always get full scholarships and the only need-based aid they'd ever get would be a Pell Grant...they'd never get institutional financial aid because athletics is supporting them fully.

Other sports are "equivalency" sports, where you have a pot of dollars to give (based on a number of scholarships), but you can divvy them out to as many/few athletes as you like. Academic scholarships do not count against that limit (provided you can show that the scholarship is purely non-athletic in nature and available to all students). Probably more importantly, lots of these students are eligible for need-based financial aid (again, as long as the rules are the same as for everyone else)...in the equivalency sports, it makes sense to use institutional need-based aid, because it does "save" you athletic scholarship $$$.

So a poor star soccer player can potentially go to Stanford for free without using any of the athletic scholarship money...while he/she would probably require use of at least a half of the allotted athletic scholarship $$ at VT.

They are absolutely using non-athletic aid in place of athletic aid...which anyone can, but they have much more capacity to do so. As for "2X the total scholarships" that kind of depends on semantics of whether you consider need-based aid as "scholarship"...if you do, I have zero doubt that a school like Stanford is giving out 2x what VT is (probably a lot higher than that)