In some paradigms they consider it fasting up to 300kcals a day.

In some paradigms you are not even allowed to drink water and call it fasting.

The word fast means multiple things.

That is certainly the purist view. I just came off a 3 day fast and in that time I had some Benfotiamine, B-50 complex and Magnesium. Despite having zero calories and zero insulin impact they do have an impact on the bodies metabolism so a purist would also say I broke my fast but I reject that reality. Some of the times that I have fasted longer 5 to 7 days I also had Krill Oil (5 calories) and that also would break the fast according to purists. 5 calories are not going to shut off fat burning when I am in a 2700+ calorie/day deficit by BMR. When I actually break my fast I can feel the changes in the gut, mood, Ghrelin production, etc... Admittedly I am basing this entirely on a gut feeling. Either way my end goals are accomplished burning some fat, improving my overall feeling of wellness, improving my sleep, improving my vision so it works for me.