That does reference this NBER working paper at https://www.nber.org/papers/w25314 . Note that math is cheaper than English to teach, which is not that surprising, but does suggest that (once again) the “STEM” label may be an overgeneralization.
But it is true that subjects with expensive labs or other equipment, or which have to compete with non-academic employers to hire faculty, will generally be more expensive to teach than those subjects which do not.
Perhaps a student shift to more expensive subjects is a less-recognized factor in college cost growth. Some schools do charge different tuition levels by major, but that is not that common. Some do charge upper division students higher tuition, reflecting the higher cost to teach upper division courses, but that is also not that common.
Regarding University of Washington in particular, note that the list of majors at http://www.washington.edu/uaa/advising/degree-overview/majors/list-of-undergraduate-majors/ shows which majors are capacity limited (i.e. more interested students than the department can teach). The arts, natural sciences, and all of the more pre-professional divisions except for the College of the Environment tend to have more capacity limited majors, while humanities (non-arts) has none, and social sciences has a few (including economics, the usual substitute for business).