The title of the book is incredibly misleading. Buddhism is not mindfulness + the insights into the human condition mindfulness grants. Buddhism without the reincarnation, the other planes of existences, the deities, the rules for living, etc. isn't really Buddhism. "Why the Buddha was right" might have been better.
I haven't read the book but from the article it does seem like they are simplifying Buddhism quite a bit. They left out the part about meditating on becoming a corpse too. That might be the best part! (this comment may or may not be sarcasm :P ) That seems to be the thing lately though, take the parts you like from something, and leave the parts you don't, especially with eastern religions.
I think of Buddhism as fact because it's hard to argue some of its philosophy. Life is pain. It's either less pain no pain or all pain at different times. Trying to avoid pain can create all human suffering but that too has necessity, refuge from pain. These are some alien notions to westerners. Which can obscure their fundamental truth
The thing is, Buddhism itself and its underlying insights are disappointingly different. Buddhism has hells, gods, ghosts, Buddhas who lived for thousands of years and were hundreds of feet tall, "Celestial Buddhas" that live in other realms, and other such things. I agree with the things you mentioned. In that sense, I see Buddhism as fact too. I love the mindfulness-related parts of it. It has changed and is changing my life. But when you say you see Buddhism as fact, it's unclear what you include and what you don't.
The article is correct in identifying a clear separation between religious Buddhism and therapeutic Buddhism. I find most Westerners underestimate how very, very similar Buddhism is to other religions in practice, because they assume religious Buddhism resembles the therapeutic Buddhism which is so popular in America. In reality, religious Buddhism is as varied, ritualistic, and even as anachronistic as Abrahamic religions. (The anachronistic description is my probably wrong perspective on all religions, but it is true that if you consider Judaism outdated, than you should also consider Buddhism outdated as well.) The four noble truths especially are not something most religious Buddhist incorporate into everyday practice -- it's usually more about chanting for death points and other ritualistic things.