yes but it doesn't get down to the root issue. if an otherwise healthy adult lifting heavy, HIIT, additional cardio is still gaining weight at 1200-1300 calories then applying an age old 500 calorie deficit just no longer makes sense. 700 calories for anyone is just... crazy.
I will preface and say this may not apply to her but:
Is she weighing herself 5-7 days a week first thing in the morning, in the same clothes, after using the restroom? Are you then using a trend line to determine she is in fact gaining weight over this time period based on the trend line? I ask this because for smaller people who are less metabolically active, the old school method of weekly changes may not be as reliable. A lot of coaches I know use bi-weekly comparisons for weight loss for smaller people.
This is because for a smaller person, they are rarely using a 500 cal deficit. As you pointed out, its just too much in proportion to their caloric needs. In a relative sense, its kind of like crash dieting. Most coaches now advocate for a rate of loss 0.5-1% BW per week. If she weighs 140 lets say, that is 0.7-1.4 lbs of weight loss per week as a goal. On the lower side, 0.7 lbs can be tough to see over a single weeks trend, but over two weeks, it should be easier to see 1-1.5lbs lost. To lose 1-1.5lbs bi-weekly, that is a 250-350 cals deficit. So 500 cal deficit can be a quite extreme approach for smaller people. However, when we work with smaller numbers, the room for error is less as well.
People are usually not good at tracking their intakes. Even in registered dieticians, there can be a 20% error rate on average. For more common folk, it can be around 40% even. This would mean that a tracked 1200 could really be 1440 cals due to error in well educated people in food tracking. For a bigger person, like a 200lb male, this is much less of an issue, but it is more of real world problem for a smaller person less metabolically active person. As this simple variance can wash away a smaller deficit.
Next, food labels can be legally up to 20% off in the USA. Meaning a food labeled at 100 cals a serving, can really be 120 cals a serving. Some of this can contribute to the tracking error above, so its not all just people stink at tracking food. This is also a larger issue for sure for smaller people.
Add in someone being genetically prone to metabolic adaptation, and you have a scenario where one appears to be doing everything right, but nothing is happening. I personally do not look at caloric intakes on a food tracker as accurate, they are generally precise though baring in mind the errors we just have to accept in this case. So instead of viewing 1200 tracked cals as her "maintenance" I would rather just aim for that number daily to be precise, as it may not be accurate. So if she is tracking 1000 cals, is that the accurate number she is eating each day? Very likely no, but if we hit that daily, it will generally be precise. I would try to create more of an error buffer in her tracked cal goals to help account for the very likely unavoidable errors present. So I would aim for less tracked cals, but the number really is not accurate anyways. I hope this makes sense.
The last thing to consider is that she can be gaining muscle right? One pound of muscle is only made up of about 700-800 cals where a pound of body fat is estimated to be around 3,500 cals. This means that when one is in the early stages of their muscle building journey, the scale can move up at a rate that may be unexpected due to muscle gain. This also means that recomp, the loss of fat but gaining of muscle is mathematically best done in a slight deficit. This could explain some aspects of the lack of scale changes. It is best to remember the scale is just a proxy for her goal of fat loss and body recomp. To help round out her object proxies for her goals, why not add in a waist measurement done right after she weighs herself? If the waist number is staying the same while her weight is going up, that usually indicates muscle gain. If it is going down while her weight stays the same or goes us, that means she is likely recomping.
My GF tracks both her weight and waist over time, she is a general fitness person. Whenever she is sad about weight gain and when dieting things are not going the way she expected on the scale, checking her waist trend and performance metrics on her key lifts that she trains near failure in the 5-30 rep range have multiple occasions shown objectively she has gained muscle and improved her body composition, regardless of her scale weight. That does spark the idea that is would be good to have her log key performance lifts/cardio metrics, another proxy for results.
Also, the research at least suggests that low carb and IF really dont do anything special metabolically. When cals and protein are equated in studies, they see the same effects compared to other diet models. What this means is that I would not be surprised if a low carb 1,200 tracked diet and an IF 1,200 tracked diet do not result in any different results from pretty much any other 1,200 cal track diet over time. Low carb can be a way for some people to control their hunger better due to food choices and ketones. IF can help some people control their hunger due to limiting the window in the day they can eat. Outside of diet adherence, there is no reliable human clinical end point data suggesting they do anything metabolically compared to other diet models when cals and protein are equated. This has matched my experience and those of I have coached and helped.
Not everything is as it seems sometimes. I could be off, again I am happy to admit, but I dont think it hurts to account for likely errors and expanding our tool box of objective proxy markers for results.
If we are worried about her metabolism being slow, then I would personally, IMO, suggest the need to investigate things that impact the calories out side of the equation that are more related to BMR. Like sex hormones, thyroid, cortisol, and the combination of CRP+leptin.