My Opinion: If you attend a super rigorous/top school, and you have a marginal GPA, adcoms will give you a second look. No guarantees, but a thorough second look. I think a high GPA from anywhere is viewed as such, while a low GPA from a less rigorous school is really hard to make a case for.
BTW, 3.1 is below marginal (I'm talking between 3.3-3.5) and UW isn't typically included in "most rigorous undergrad" lists.