Does muscle burn fat locally, or does the presence of muscle burn fat generally across the entire body?
Muscle does burn stored glycogen locally. It may have a preference for some other local nutrients from fat tissue or other tissue as well including lipids but at most that would probably only deplete the cells and then cause exhaustion. So it probably won't actually burn local fat cells, only the stored nutrients inside them. The body will at the same time be working to pump new nutrients into the storage in the depleted cells in the muscle and also the subcutaneous fat if required. So generally your body can redistribute nutrients (on average) as fast as you burn them and make up for any shortage while you sleep or rest. After all you can't exercise constantly. However it is totally possible to reshape your body, even your fat distribution. Same idea but different methods involved.
Your body is amazingly adaptive, see my Quora blog for examples of the amazing things it is capable of through just basic exercise without equipment: Basic personal fitness. I link specific posts of my blog for reference so you can wait for that if you want but the blog will eventually get new posts as well.
Technically you can't burn off fat in a specific isolated area, without impacting other areas, at the rate of starvation or anything even near that speed. However you can change your body fat distribution slowly and gradually over time by changing the underlying muscles, mitochondria and presumably hormone or other signal production (naturally). So in a way that is "spot reduction". I have personal experience with this type of "spot reduction" in terms of changing my fat distribution (without losing fat in total or even while gaining fat) and also in terms of getting rid of visceral fat. It takes years of daily hard work to achieve big results so this isn't any kind of instant gratification thing. For a big long personal story and my extended theory about that see my Quora blog post: How do you stay healthy even if you have a high percentage of body fat? by Noah Harmer on Basic personal fitness .
The term "spot reduction" has an undeserved bad reputation because of lots of scammers in the fitness industry trying to sell people fitness programs and instant gratification and telling people they can "burn off the fat" in undesirable areas fast. They make it sound like it will happen as fast as you could lose the fat to starvation which is usually not so. The fastest it can happen is as fast as you can build muscle and mitochondria. Now for people familiar with gaining muscle they know that new bodybuilders can build muscle the fastest. However for more seasoned bodybuilders gains become harder to come by. So these fitness programs may be trying to exploit the beginner effect or whatever you want to call that. That means they certainly won't work for everyone if they even work for anyone at all. Many of these programs are probably frauds but are relatively unregulated. Proving the fraud conclusively in court would probably require an expensive medical study be performed on the specific program for just such a purpose. Some of these programs may even work for some people on some diets with some body types. Some programs may also be genuine, specially if they don't promise instant results and expect you to work for years to grow larger muscles with high mitochondrial density. For a program that works for you individually you really have to design your own or at least mostly design your own. Everyone has a unique individual body and starting point after all.
That's what I encourage people to do. Along with a core set program that only takes up 1/3 of their time to ensure strength and aerobic exercise and a certain minimum amount of work and general fitness. For more information on that see: Calisthenics and Stretching by Noah Harmer on Basic personal fitness . I'm not promising any gains. I have personally observed very slow but real spot reduction of my visceral fat or change in distribution into subcutaneous fat on other parts of my body. Either way my pot belly is getting smaller and my waist thinner while my weight remains steady. I don't think I'm losing much fat, maybe a little is being replaced with muscle. I'm certainly not losing subcutaneous fat as far as I can tell. It's been about a year so far of regular daily work with heavy focus on sit-ups and abdominal exercises (that's all I started with). I may also have sometimes been working harder than I advise in my blog but I did try and suggest the time was flexible to suit individual needs. I do a set number of exercises or more for bonus rather than timing myself. My current daily challenge to myself takes maybe 20 minutes but I'm working to reduce the time and sometimes I've been done my previous daily routines in about 5 minutes before ramping up to a new challenge so 15~ minutes is just an estimated average like I say. I can't promise you the same results as you have a different body and all that. If you can adapt a similar program with similar focus on aerobic core fitness and goals for improvement for your own use you could probably either eliminate or prevent visceral fat in a similar way while allowing yourself to maintain or build up subcutaneous fat. To prove you had prevented it you'd need to gain weight and build up muscle and subcutaneous fat without visceral fat. So hard to see results if you don't have much visceral fat to start with. I can promise that it's good exercise though. Good for your aerobic fitness and all that as long as you don't injure yourself and aren't already injured. I think this program probably fits the "recommended" guidelines for 31~% mortality reduction from exercise as per this chart: