"Would admissions committees at elite law schools take her seriously? Would they see “public relations” and downgrade her? Would her transcript carry less symbolic weight than one in philosophy, political science, or history?"

Nah. All law school admissions committees care about are uGPA and LSAT / GRE scores (for the 1/3 or so of law schools that also accept the GRE). They don't care what you majored in. They don't really care about you at all beyond your ability to qualify for federal and private student loans; it is the rare law school that requires an interview, and most give but the most cursory attention to whatever essay(s) they require. Only the numbers matter, because the numbers are so crucial in the rankings, which in turn are so crucial in elite employers choosing to recruit on campus or not. For many years there was grumbling about how law schools engage in soft discrimination against STEM majors, as their uGPAs tend to be lower.

Numbers uber alles. Remember when Princeton shrugged its shoulders in the early 2010s and gave in to grade inflation? One of their public justifications was that grad schools (and employers) expected higher GPAs from Princeton students than what they saw. In an age where grade inflation allows the top few dozen law schools to have 3.9x as their median uGPA, even mighty Princeton could not get away with a median of 3.4 or whatever it was. It didn't matter that it was Princeton. It didn't matter that they are one of a handful of schools that make every senior write a thesis. It only mattered that Princeton Number Lower Than Harvard Number. Goodhart's and Campbell's Laws always, always rule the day in law school admissions offices.