The rim is a propriety alloy mixed by BBS and formed in Germany as a cast product. It is "flow-formed" and heat treated, ending in a paint like process that covers the entire wheel in a thick powdercoat like durable finish.
The only current production street wheel that is magnessium is the Porsche Carrera GT (Porsche requested Magnessium to give it supercar status and set it apart from the GT3 and GT2).
You should always be very careful with attempting to repair wheels for several reasons. Comments below are specific to BBS wheels, but can apply to other brands as well
-Alloy makeup is a proprietery mixture and varies from wheel to wheel. The repair shop will not be able to match it, therefore the weight properties and strength will always be off, even if repaired to perfect dimensions.
-Since alloy make-up can't be matched, a weld will never be fully attached, creating a weakspot
-The flow-forming process BBS uses compresses the cast material under heat and pressure (similar to a forging process) to stretch the outer rim and reduce outer rotating mass. Yes, it's possible to heat with a torch, bend back to original shape and make it look like new. However, the structural make-up of the wheel is now compromised as you've heat treated it and weakened it.
-Even when fixing the paint on a wheel, you need to be careful. Chemical paint strippers can attack the alloy and weaken the wheel. Using a heat gun to strip, or heat to cure the paint will weaken the wheel. Powder coating is one of the worst things you can do to a heat treated wheel.
-Each time you heat cycle the wheel, you are getting up to a 30% reduction in structural strength...EACH TIME!
-Driving day to day may be ok on a repaired wheel, but in a car that's designed to give you 100% performance and go to the very limits of safety, do you want a wheel that's only 90% or 80% of original strength (or even less) when you're going 150+mph? Wheels don't normally fail just sitting in a parking lot or even driving at normal speeds...but at 170mph a failure of your wheels is going to have catastropic results.
-BBS's official policy is their wheels can not be repaired, any attempt to will void all warranties. When a wheel has reached the point where it needs repair, it should be discarded and replaced. This isn't to just sell more wheels, there are valid safety concerns here. Dealers who offer to repair, or independant shops that do the repairs are returning a product that is not 100% of the product that you originally had.
I'm not suggesting you attempt to repair your wheel, however if the shop you are talking to asked you if it was magnessium or aluminum (a good shop could tell just by looking at the wheel's stampings), run aways and find someone competent!