I agree that a supplement to the cookbook would be useful–one that lists the brands of “packaged goods” that are safe or includes recipes for things you need to make yourself. I have found many recipes in the cookbook that I like and make frequently, but I shy away from those that use the products you listed. For the reasons you stated, I would not recommend the cookbook to someone just starting out on the diet. “The Gluten-Free Almond Flour Cookbook” by Elana Amsterdam and “Grain-Free Gourmet” by Jodi Bager and Jenny Lass would be better as beginning books.
I'll post the recipe I use for Worcestershire Sauce in the “recipes” section of this website. I found it on epicurious.com.
Wild rice is okay to use. It is a grass, not a grain. Any other form of rice, though, is taboo. I've used packaged chicken broth for the wild rice recipe (Pacific Organic Free Range Chicken Broth), but it's a gamble as I haven't researched the source of the “organic chicken flavor” listed in the ingredients…. Probably better to make your own or use water.
I don't recall a reference to arrowroot in the videos, but it's been awhile since I saw them, so I would be interested in the answer to that question also.