Well... fat burning machine. I have no qualms with the idea except for one stipulation: the populace can only acquire the services provided at clinics with doctors trained to administer the treatment.
Mechanically speaking, I can only think of two ways to actually retrieve the fat, both of which have been mentioned. Using hormones to cause fat to leave cells where it is then some way or another eliminated from the bloodstream, or an incredibly invasive surgery involving slicing open adipose tissue. Given how if people were willing to go the second route, they'd probably be fine with surgery, I guess we're all agreeing that only the first way would be feasible for everyday treatment.
My main concern is how the increased fat in the bloodstream would affect the health of the patient. While I don't have the scientific background of some people here, it does seem to me that if a hormone is added to the blood that stimulates the release of fat, the body rest of the body wouldn't be prepared -- I assume that when actions like that are taken naturally, there are some changes in the blood vessels and tissue the nutrient is being directed to. I would think it would cause increased risk of strokes and other afflictions related to clogged blood vessels, so the machine would have to be operated in very small increments. Assuming that this is taking place in a medical setting, as mentioned before, I would expect it to be nearly as much of a time waster as going to the gym, without even the other health benefits of working out. It also would cost more for the patients, given how they'd have a doctor charging them for the time spent have fat removed.