I agree that when you actually exercise that you will expend more energy, and that their will continue to be a slight raise in metabolism for a period after you've stopped exercising, which is the factor that people keep banging on about. However, as discussed previously your body is little more complex than just burning fuel, we store energy as body-fat for a reason, and its not the reason people assume (i.e we've over eaten). It is possible to have a raised metabolism but that comes from eating enough you may also continue to expend energy at a higher level.
When you try to go into a negative balance, i.e the old calories in minus calories out equation, your body has to protect its body-fat stores. Its job is to assist you in times of need, so yes the body will use it as fuel when you increase the demands its under. It will also make a mental note of this and if you continually keep doing this it will adapt to protect itself. Sadly in the simple world of Personal Training this is typically not understood. Or maybe it is and they just realise that they have a client that will always need to exercise at increasing levels to stop the fat storage. The body adapts quickly to ensure its ready for this energy expenditure the next time you put the body through it again. The metabolism slows down and you become more efficient, you make your energy last longer. If your reading this with your PT and your weight dropped slightly when you began training, but has now mysteriously hit a plateau then re-read this and start asking some questions.
Their will no doubt be those of you twittering that its weight training that raises the metabolism, and your right it could as muscle is indeed more metabolic. Sadly any increase in muscle mass and activity needs accounting for in the amount of energy you consume. Boot-camps are springing up everywhere (I've even seen former gym haters being convinced its beneficial), and it really does baffle me. One of my clients attended one regularly before seeking my help, surviving on 1500 kcals a day and masses of exercise did have the effect of loosing some weight (it would be interesting to of seen the %'s of muscle and fat tissue lost), sadly the moment they stopped it all came back + more.
So, yes they do increase energy demand, yes people may increase muscle mass and maybe even loose body-fat. The maths just doesn't add up though, sure you intend to keep up this new low calorie, fast paced aggressive lifestyle. The increased metabolic activity leads to a drop in metabolism as the body protects itself against the increased demands its under (usually while also being dealt the blow of less food). How will you or your PT tackle this plateau? No doubt they'll increase your work-rate or demand that you cut back on your energy (food) intake. The may even go as far as banning carbohydrates to try and kick start the fat loss. This is the point at point which I met the client mentioned above, injured (shoulder, neck, low back, shin splints), suffering emotional problems (depressed, anxiety) and to top it all of back to square one with their weight. I met my client when they approached me for advice about injuries and wanted me to help fix them so they could continue the relentless pursuit of 'weight-loss' in the gym. Its interesting to note that a lot of PT's eventually become trained in sports massage therapy as they no doubt attempt to keep them clients on the exercise merry-go-round.
Creating this calorie deficit (either dietary or exercise based) means a constant battle to stay on top which can be seen in gyms and diet clubs throughout the country. For 99.9% of people we are likely do loose focus and not have the ability to continually increase the energy demands and burn more calories through exercise. Willpower won't be enough, fatigue will kick in and our hungry bodies will convince us to skip a day and the slow decline will start. For those that do continue on relentlessly, they run the gauntlet of injury and illness, a tired energy depleted body is wide open to both. You only have to look at research on athlete recovery times for viral infections. I also see a lot of people on facebook who are always jogging, doing aerobics and consequently always blowing snot from their noses. Either way most of us will not be able to keep up the relentless (senseless) quest to increase either the intensity (harder) or volume (longer) of our exercise to keep ahead of our metabolism.
If you want to get fatter then Exercise and Dieting is undoubtedly the most effective way to do it. Unless your eating enough to counter the energy demands upon your body, you simply become an efficient fat storage machine.