Listened to him again; I'm going to say that these girls who are dieting at 1000 (he says 800 at one point) and working out for 2 hours a day? Are either lying about their calories over the course of a week or not really aware of what they are eating, regardless of how "damaged" their metabolic rate is. Then he starts talking at 1600 calories and I go "OK, this is probably right!" But the 1000/800 calorie girls not losing weight? They are not accurately reporting their calories/outright fabricating their intake.
I mean it is probably an issue with people who have weight that fluctuates between normal and low body fat%, but if you are legitimately consuming 1000 calories a day and not a sloth? Something is wrong about the numbers being reported.
Edit - Probably came out a little harsh~ I feel like the most likely situation in lindz (and literally every one of those people who report they can't lose weight on 1000 calories + cardio every day) is very similar to Brahmas. It is not understanding the amount of food/calories you are actually consuming on the daily over periods of time. If you only consume 1000 calories in a day and spend 20 minutes a day doing -any- light exercise? If you are above 3 feet tall and 80lbs, you should feel fatigued as shit all the time, ketosis or not, as well as feeling incredibly/debilitatingly hungry. Like, to the point where you have issues doing daily activities. So odds are, you aren't consuming just 1000 calories, and you should spend some time accurately cataloging what you eat each day and try to more accurately calculate your daily caloric intake based upon that catalog. It makes it a lot easier to give meaningful advice.
If you -are- legitimately consuming 1000 calories a day along with even light activity and unable to lose weight? I would recommend seeing a health professional that specializes in dietary nutrition, because you are an incredible outlier that standard science has issues explaining, regardless of what a personal trainer might say.