You are right, of course. Without quantifying (how low is "low calorie"?) these statements are useless.
There was an experiment in Mass General some 15 years ago, in which they were able to get people with similar lifestyle/activity on 1500 cal/day diet. About one third lost weight, one third stayed the same weight, and one third gained weight, depending on how exactly the diet was composed.
Yes, you will lose weight, regardless of diet composition, on less than 800 kcal/day. Is that "low calorie"? "too low calorie"? "moderate"?.
No, you will not necessarily lose weight on more than 800 kcal/day. You probably will if your diet was not specially crafted to make you keep your weight on 800 kcal. When you get up to the 1200-1500 range, there is a non-negligible probability of "accidentally" gaining weight (or at least not lose it) by randomly stumbling on a bad diet composition.
One of Cabanac's (If I'm not mistaken) experiment was able to make rats gain weight for 3 weeks on a diet of water+chalk (caloric value 0) for a while, by feeding them water+sugar+chalk for a while, and then dropping the sugar. Sure, it was water gain - but the calories in - calories out theory fails so miserably in this case (and countless others) that it cannot be taken seriously. (For only 3 weeks for a rat; it might not hold for a human for a few months in similar conditions).
The calorie accounting is an approximation at best, which possibly takes several months to a year to average out reasonably, whereas a lot of the research focuses on results over 3 months or less.