It’s likely that Ms. Shields (and many other Princeton and other Ivy League undergraduates) fulfilled many of their distribution requirements with AP credits or college credits otherwise earned in high school.
The courses listed on my daughter’s Mount Holyoke transcript shows no evidence of the college’s language, freshman comp or math requirements — she took enough college level Russian, a college level writing course and AP calc (getting a high enough score on the AP exam) while in high school to fulfill them before she was even admitted.
I had thought about that. Congrats to your daughter. Wow, Russian, that's quite an achievement.
We did a similar thing call Dual Credit, our son took all his high school credits at the community college, actually never set foot in a high school, and received his AA and High School Diploma at the same time.
I know they have more and more programs for kids to get a leg up on their college work. The Dual Credit program was so popular that now they have High Schools on the community college campuses, they call them Collegiate High Schools, plus we have the IB programs and AP classes (my husband and I both wish they would have had similar programs back in our day.)
So on my son's college transcript from his University where he received his BA, you wouldn't see a lot of math, even though he took lots of math.
Also there is the possibility that Ms. Shields CLEPed her general requirements. I knew someone who ClEPed out of 75% of her General Requirements.