The Bear River Campground\Day Use Area is a state park I believe. I am not 100% sure about your rights in a state park, but I do believe they are far more limited than that on federal public lands. I haven't done much research into state parks, but with the knowledge I have, I wouldn't run any kind of pump in a CA state park, especially one that had a posted sign saying I couldn't. If I had the desire to do so I would do the research and go from there.
As far as the Water Board and that FAQ goes, there is no Water Board regulation specifically pertaining to highbanking. That FAQ puts highbanking against current general water board regs. If you think those regs stop you from highbanking then I'm not sure how you think you can run a stream sluice, use the river water to classify, pan with it, filter water to drink, take water for camp use or basically anything that even remotely involves you removing water or any mining activity other than maybe drywashing.