Not true. I've been sourdough baking for some time and am a reformed home brewer (it was taking over my life LOL).
I have a very active starter (Friends of Carl Oregon Trail starter; also used int he recipe below) and I use it regularly, with many types of grains. Now to the point: wild yeast (Candida and other genera) and various Lactobacillus species (which is what every sourdough starter is) won't thrive when changing grains. Most of the time it simply dies on the spot. I see posts where people think their sourdough starter brew is dead, that's because it was dead, and some other strain of yeast took over. There is no brewer's yeast nor baker's yeast (Saccharomyces cerevisiae) strain in a sourdough starter. In fact they die if they get into a starter since the acid produced by the Lactobacillus kills them fast.
So, with all this in mind, there should be a way to convert a starter raised on white flour (I actually don't use any, mostly white whole wheat or red whole wheat) over to the grains you will be using for the beer. That's where I think the extract method may run into trouble. Using an extract to nourish a starter may or may not work, my hunch is that it would fail. It certainly wouldn't survive in 100% extract. It would survive in flour made from barley if it was converted over very slowly (by feeding it with a tablespoon with a cup of flour, then gradually substituting barley flour for the wheat flour). It would not survive in ground up barley, it's simply too coarse and the starches aren't very accessible to the yeast.
I was looking for a real sourdough yeast brew (no beer yeast like the above recipe, which doesn't have anything to do with sourdough IMO). I think I'll try a dumbed down version of this recipe:
http://www.betterbeerblog.com/index.php/2011/12/27/homebrew-session-experimental-sour-dough-ale/
He didn't try to convert his starter so I think his experiment went south from the start. What he actually got probably wasn't a beer fermented by the starter, but with some other strain of yeast (or a miracle could have happened and the sourdough yeast survived) and the Lactobacillus simply died off.
Does anyone have experience with using barley flours, not whole grains, in a wort? I am an idiot when it comes to making my mash, I have only used extracts and the grains just for flavoring.