I don’t have any primary data at hand, but I suspect you are right. Most colleges started after Labor Day back then, and many not until mid September. And it was customary to have the summer schedule in the early part of summer, leaving August free for faculty vacations.
As it happens, I was teaching at Seattle University in 1968. I don’t know what the UW schedule was for sure, but I would guess, fairly confidently, that they would not hold clsses in August. No university did that back then. It was only in later years that they began starting fall terms in late August. But in the 60s, starting before Labor Day would have been extremely odd.
Ha! Having lived in the Seattle area for 5 years, I'd say that the reason for having August "off" is because that is the only "summer" Western Washington sees. I spent many a 4th of July huddled under a blanket with a fire roaring in the wood stove! You can't depend on it to be warm until August. Of course, you learn to find beauty in cold, drizzly rain, but that's another story.