fast heart rate w/o exercise= calorie burn?

If she says that pills are giving her an elevated heart rate, she is probably taking a stimulant. Some stimulants will suppress your appetite and cause you to lose weight (Adderall) while other stimulants like Ephedra increase your metabolism as a thermogenic agent (increasing your 'heat' as a biproduct of burning off a bit of extra fuel). Many diet pills are just loaded with Caffeine (Hydroxycut) and other non-stimulant pills will change the way you metabolize fat without increasing your heart rate.

Note that all of those stimulants I listed with MAYBE the exception of Hydroxycut are dangerous (and in Adderall's case ILLEGAL) to take without the direction of a physician. I personally wouldn't take any diet pills...might as well rip out your liver and take a sledgehammer to it because that's how far you'll get.

If your friend is taking a pill that makes her heart race and she's using it for weight loss, she must be doing so under the supervision of her doctor. I know I might get a slap on the wrist for bringing up the A-word but it's a very dangerous and awful drug to get involved with if your doctor is not aware and able to guide you. If you notice your friend changes in personality (becomes more withdrawn, irritable, starts keeping weird hours, develops repetitive motor tics like hair-touching, itching and picking at her skin or starts neglecting hygiene) you should approach them about it or go to their loved ones.