I don't think that there is any real "cure" for IBS. There are ways to keep it under control, but saying that eliminating dairy or other food products would "cure" it is misleading. A cure would mean it would be completely cleared up and gone away and that you'd be able to eat whatever you wanted again, including dairy. So I think cure is the wrong word. After all, you can not cure an allergy, you can just avoid what triggers an allergy attack.
I'd have to say that I disagree with whoever the MD is that wrote the book you are currently reading. Everyone is different as to what triggers IBS flare-ups. There are lots of food culprits that IBS'rs have in common, but there are also many culprits unique to each person. Plenty of people do have trouble with dairy, but I don't think it can be said that IBSr's are all allergic to all types of dairy. I have IBS-D and I can eat some dairy. I can safely and comfortably eat cheese, yogurt, and milk in my cereal. I can also tolerate ice cream as long as I do not eat it on an empty stomach. I know for sure that I have IBS and I also know for sure that I am not allergic to dairy. On the other hand, there are people who are allergic to dairy (lactose intolerant) and do not have IBS.
Yeast overgrowth is a known factor in causing stomach problems, but I believe yeast overgrowth is a totally separate problem from IBS. The foods you listed as contributing to yeast overgrowth are sometimes known as triggers for IBS, but perhaps not due to the yeast in them. I think caffeine is a problem because it's a stimulant, which makes D worse. If you think you have yeast overgrowth you can go to a doctor and I believe get tested for that. A yeast overgrowth can be resolved with treatment, but that will not necessarily cure IBS.
I hate to say this, but don't get your hopes up about
totally getting rid of the IBS, if that's what you have. You will only get frustrated. What works for others may not work for you. Working out a safe diet is trial and error. I know for me I have discovered that raw fruits and veggies, fruit juice, alcohol and spicy and acidic foods are problems. I can, however, comfortably eat some dairy and some bread. If you'd like to modify your diet I would suggest start eliminating certain things to see if the symptoms subside.
Good luck! It can be frustrating but once you've got it figured out, it can be kept under control.