In order to get meat cooked, you have to heat it. As you probably remember from physics, and experience in everyday life, heat exchange is only present where two surfaces touch (this is why vacuum is at absolute zero, there is nothing to touch there). You can actually heat things without touching, but you need radiation for that. Your microwave is capable of it, but not a kitchen stove or an open fire, and I'll assume that you don't fry chicken filets in the microwave. So we are talking heat exchange between two mediums here.
In a case where a piece of food is laid in heated oil, all the oil has roughly the same temperature. The portion of the food which is submerged in the oil exchanges heat evenly everywhere (note that the food does not directly touch the pan when there is oil in it, so there is no direct heat exchange between pan metal and food). The temperature of any point of the meat is only dependent on its distance from the meat surface. This is known as frying.
Of course, if you are frying at a high temperature in a shallow puddle of oil (like in a pan), the oil trapped between pan and food is hotter than the oil on the side of the food. So the food gets hotter quickly on the bottom than on the sides. This is still suitable for either flat items (your filets) or small items which are turned often in order to let all sides of the food spend some time at the bottom (stir-frying them). Still, the stuff doesn't get fried as evenly as it would be in a deep fryer (where the food is swimming in the oil, and the oil is heated from all sides).
When you have an item which doesn't contain any significant amount of fat (very lean meat or a slice of a vegetable), you don't have heat transfer between oil and food. What happens depends on the temperature.
If you use low temperature and no fat, the juice from the food flows out, but does not evaporate quickly. It forms a puddle. This puddle acts in the same way as the oil in the previous example, so you have a heat transfer between the submerged parts of the food item and the juice (mostly water), which is as even as in the case with oil. When you are using this method, you are simmering the food in its own juice. This is quite tasty for some veggies, e. g. zucchini. With meat, it is another thing. When you bring the stove temperature up, the juice doesn't get hotter, it just evaporates quicker, but it stays at evaporation temperature, which should be slightly above 100° for salted water. So your heat exchange is between the cold medium (food) and warm medium (juice at ~100°C). This temperature is quite enough to denaturate the proteins on the meat surface, but not enough to produce Maillard reactions, which happen at about 150°C. The inside of the meat is heated by the surface heat propagating to the center (heat conduction on the microscopic level). As meat is not such a good heat conductor, this takes quite some time at the relatively low temperature of 100°C. So you can only use this method for very thin meats. When they are thick, you'll have to either pull them from the stovetop too early, leaving them well done on the outside and underdone on the inside, or let them stay until they have cooked well on the inside. While the temperature is not high enough to sear them badly on the surface, they lose too much juice during the long cooking time, leading to unappetizing dry meat. (The reason why this is not a problem with the zucchini is that 1. Zucchini are sliced thin, and 2. Zucchini don't taste too bad if they are undercooked on the inside, meaning that you can pull them off while still juicy).
So what happens if you have a very lean meat and turn the temperature up? You don't have a fluid for heat exchange any more, as there is no fat available, and juice evaporates quickly. Your heat exchange happens between pan and meat on the bottom, and then there is secondary heat exchange when the pan heats the air around the meat and the air heats the meat. This effect is relatively weak, because air is a fairly good heat insulator, and the heat from the pan will char the bottom of the meat badly before the air cooks the sides.
In this high-temperature no-fat scenario (usually known as grilling), heat transfer to the (bottom) surface of the meat is very rapid, more so than cooking and pan-frying. The rest of the meat is again heated by conduction, but the proportion of the heated area is smaller than when frying, and besides, metal-to-meat heat conduction is much quicker than outer-meat-layer-to-inner-meat-layer, so you get a much bigger heat difference between meat surface and meat center than when frying. Besides, the surface temperature of the meat is hotter than when frying at the same stove setting, because no heat is absorbed and dissipated by oil. So you get a much bigger temperature gradient in your meat, with the surface very hot and the inside quite cold. If your meat is thick, the surface will turn to coal long before the first protein in the center denaturates.
So where does all this physics leave you when all you want is a tasty supper? I'd say that tradition has it best here.
Grilled meat can be tasty, but a pan on a kitchen stove is not the best technique. If you make it hot enough, you'll end up with undercooked, charred meat, and if you reduce the temperature, it may be still OK, but it won't taste great, because it will be too dry. So don't use a hot stove without fat. If you want grilled meat, use a grill.
Cooked meat (in a soup) tastes OK (but better if you braise it first), but cooking meat in its own sauce does not. It gets hard and dry. So the verdict on no oil and low temperature: just don't.
Which leaves you with the fat options. Of course, you don't need to submerge the meat completely. Half the height is enough because you'll turn it, and somewhat lower is also OK, because the conduction is still enough. If there is enough fat present in the meat, don't add any. But if you want to fry a lean meat, add fat. The temperature you use should be high enough to quickly warm the surface, at least enough for a Maillard reaction (this is when meat turns brown and crispy, produces most of the aroma associated with high heat treatment of meat and carbs) and low enough to allow for the center to be cooked before the surface is burnt. So the more well-done you like your meat, the lower the temperature you should use and vice versa.
Don't worry about the calories when frying, unlike some veggies (eggplant, mushrooms), meat does not soak up frying oil. The surface will be greasy of course. But, fat is still a macronutrient, which our body needs. It also enhances the flavours of the meal, and promotes a sated feeling. If you want to keep the calories at a reasonable level, use a leaner meat (e. g. chicken breasts without the skin), fry in vegetable oil (not frying fat like palm oil & co) and put the fried meat on a cake cooling rack to let excess fat drip off.
