There are references in her book. The effects of pH and so on have been well-studied, and antibacterial mouthwashes are well-known to kill bacteria. I don't think there's been an RCT or anything of her system specifically, so that is based on her experience, but the studies do demonstrate that brushing alone is not sufficient. I'm not saying she's the last word on the subject, but it's how evidence-based medicine works - if you don't have strong evidence, you look at weak evidence such as expert advice, and I haven't found any other advice that discusses going beyond brushing. That's sort of the issue, is that (similarly to this neurosurgeon's experience) the vast majority of dentistry is focused on filling cavities, rather than promoting oral health or health in general.
Ellie Phillips is a big fan of xylitol though. The science on that is a lot less clear, e.g. how much xylitol is necessary in gum (she of course advocates huge amounts), and then she also sells mints which have little effect on plaque. (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8791908/) I sort of ignore that, just because she has to make money doesn't mean the rest of her advice is not evidence-based.
Ellie Phillips is a big fan of xylitol though. The science on that is a lot less clear, e.g. how much xylitol is necessary in gum (she of course advocates huge amounts), and then she also sells mints which have little effect on plaque. (https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8791908/) I sort of ignore that, just because she has to make money doesn't mean the rest of her advice is not evidence-based.