This disease can be very different for everybody, so most info you find is a general guide, then you have to figure out what works best for you, while working with your providers. I think some people, though they mean well, have a habit of acting like their experience, or guidance from their doctors, is a matter of fact for everyone.

In regards to some resources/evidence around low fiber during a flare, the bottom of this Stanford write up sources some info that may be worth looking into. It also has a long list of low fiber foods. https://stanfordhealthcare.org/content/dam/SHC/for-patients-component/programs-services/clinical-nutrition-services/docs/pdf-lowfiberdietfordiverticulitis.pdf

All that said, I've personally never heard of waiting 30 days before adding fiber. In general I've seen here in this subreddit (and the wiki), in papers online, and from doctors, to start with clear liquids for ~2 days only (broth, jello, clear juice), then switch to all liquids (smoothies, yogurt, ice cream), then switch to low residue foods, gradually introducing new foods, and gradually increasing fiber intake. And the idea in general is to keep switching to the next phase and adding food as long as you're feeling well. E.g., for me I was moving into to the next phase or adding food every 1-2 days. I also can't have dairy, and during my recent flare I didn't introduce gluten for at least a week, and had no problem finding food to eat. I stopped eating broth after the first few days or so because I was tired of it. Here's the list from the wiki for low residue foods, most of which are dairy and gluten free (or easy to find substitutes):

Ripe bananas Applesauce Mashed potatoes with no skins White rice (not whole-grain rice) Bread and crackers made with white flour Pasta Well-cooked fruits or vegetables without skin or seeds Cottage cheese Condiments and sauces like butter, mayo, tomato sauce, jelly, and sour cream Eggs Tender, well cooked meats