I'll cut to the chase. If you're having this problem, give your brush a shampoo. The wet dog smell should be gone. At least, that worked for me. I don't know why I haven't noticed the smell with the other soaps in my rotation: Cella, TOBS Jermyn St, and Pre de Provence. But, a quick shampooing of my brush and we're back to the same mild soap and linen smell (as others have described it) of Mitchell's Wool Fat. To provide a little extra proof, this problem and solution weren't just with one brush. I dropped my Vulfix 1000A about 6 feet onto the tile floor a few months ago, and the knot popped out of the handle. I epoxied the knot back in, but that started to loosen up after a few months. So, my repair was only short term. Finding the 1000A a little too scritchy for my tastes anyway, I ordered a 636 silvertip Omega from WCS. While I can't yet say that a simple shampooing removed the wet dog smell from this brush, I can say I have no wet dog smell with the same puck of MWF and the brand new brush.
Hope this helps others.
Hope this helps others.