The article and this discussion uses a lot of "scare quotes". Those are approximations / models. The use of the world "Chapters" isn't meant to be taken literally, it is instead meant to convey that the temporal data is chunked, probably approximated by a small set of the brain, and cached. The fact that I'm using more precise language doesn't change the fact that those are also models.

What you describe (throwing leaves to the wind) is observations. If someone were to say "The leaves swirl in figure 8 in the autumn" that is a model (autumn->figure8) that can be tested and proven/disproven. It's not useful, but it's a model of the world (autumn causes figure 8 swirls).

You can disagree that it's useful, but sorry, it's a model of the brain that is testable and refineable - look for clusters of neurons (for some def of clustering) that is responsible for storing temporal events with a clear start/stop. I'm not an expert, but probably the methods (which cause some consternation for you perhaps?) are wishy washy b/c we don't have a great way of probing the brain - we can't just throw brain cells into the air and watch them make figure 8s. That complexity and noisy input signal does not change the fact that they are proposing a model and measuring a noisy output signal to see if the model is validated or not. (or maybe model came after, in this case, but it's still testable)