Yep that's quite possible, although you can do the diet I'm on while still following Heather's EFI diet and avoiding all triggers. Before fully going on my current diet, I started by cutting out grains and that helped a lot. I used sweet potato, potato, squash, well cooked carrots, applesauce, pearsauce and banana as my SF bases, small amounts of IF, and good protein choices like chicken breast, turkey breast, white fish and shrimp. I used mainly olive oil in my cooking and made lots of homemade chicken soup (skinned the fat off the top). No IBS triggers and I gave myself a chance to see that I did better without grains.
While I do have Celiac's disease, the blood test I had for it was negative. So according to my GI I don't have it (he refused to do any more testing). My family doctor is 99.99% sure I have it. I don't have a lot of faith in the diagnostic methods and would suggest anyone with digestive problems at least try cutting gluten out for a trial period. I have seen so many people do better off grains, I would say it's worth a try as well. There are certainly lots of different SF choices on Heather's diet.