ISTM, the "Math" versus "Science" or "Engineering" thing at UW is just administrative in nature. Likely, the CS profs didn't want to be part of the EE or CompE department.
I know at my alma mater CS used to be a part of Engineering in the 1970s/1980s, but the seperation accelerated when a CS professor (who owned a lot of guns and was an avid hunter -- also quite well known as a researcher in his field) got in a fistfight with an EE professor (who was the Dean for a while). Quite a colourful story, but in that case, the administrative seperation had practically nothing to do with whether the CS program was "Science", "Engineering", or "Math" -- but was rather based on some "personnel" issues.
Strange things happen when guys who are pulling in million dollar grants end up getting into arguments in academia, that's for sure (which is why they both weren't fired -- they were superstar, contributing researchers with huge economic impacts!).