Obviously subjects should correct their underlying hypothyroidism before thinking about weight loss, but yeah, "calories in calories out" is a real thing. I've heard Peat in numerous interviews not disagreeing with this. It's why he recommended low-fat dairy, because sedentary people don't need the extra calories.
There would never be a real reason for someone to restrain themselves to 700 calories anyways, if you go that low might as well just do a real fasting protocol and get it over with.
If men, in general, are suppose to have 2,500 calories daily, then going no lower than 2,000 would be wise for weight loss. Same for women, who, in general, are suppose to be around 2,000 calories daily. Going lower than 1,500 calories wouldn't be advisable for weight loss.