Max, I think that when some people talking about "giving up privilege," they are really just using sloppy language to say "share their privilege."
Obviously, Jas never used the term "give up privilege" -- but I am familiar with the archetype to whom you allude who tend to use that stupid verbiage. Again, I think those who belong to that archetype are just poor communicators who are accustomed to viewing privilege/oppression in "ranked tiers."
Also, I think everybody (myself included) tends to lose sight of how intersectional and fluid privilege can be. For example, I'd argue that the author talking about benefitting from the privilege of passing for White is more a case of colorism than racism. When someone holds her Chicana heritage against her, *that* is racism. When people mistake her for "White" because she is a lighter-skinned Latina person, *that* is colorism.