UPDATE (Wednesday, February 4): Yes, legal.
The lawyers that can actually explain to me why this is bunk are either not explaining or haven't gotten back to me. But, from a Socratic exchange of emails with someone who should've been able to supply a straight answer, I'm figuring the whole problem out.
The problem lies in trying to prove that Amendment 52 passed two years after Munro v. Todd (which said the governor has no authority to appoint a county commissioner) gave the governor the authority to usurp the authority of the county commission.
The current RCW seems to assume this authority exists. But, I can't find any historic record that indicates that the point of Amendment 52 was to give that authority to the governor. That said, the only thing left to do is to compare the section of the state constitution before and after the Amendment to see if the changes indicate that intent.
And, by the way, in writing this out, I can pretty much say that "The Washington State Constitution, A Reference Guide" misstates it's title. It is not a great reference guide. It makes a huge mistake in implying the governor doesn't have the authority to name a county commissioner.
So, here is a line by line comparison of the 1956 version of Article II, Sec 15 of the state constitution and the 1968 version (that followed Munro v. Todd):
I'm not a lawyer, so I'm not confident in saying that the new paragraph inserted by a statewide vote in 1968 was aimed at solving the problem presented by Munro v. Todd. I also haven't been able to find anything like a history or newspaper article that says that was in the intent or effect of the Amendment.
But, there it is. This settles it in my mind, but I would also like a more definitive answer by someone trained in such things like Washington State constitutional law.