HVAC tubing is generally silver-soldered, not lead-soldered. HVAC pressures are far higher than water.
I don't think MAPP gas is hot enough to silver solder - for that you really need Acetylene/Oxygen - at least that's what I've always seen HVAC guys use.
I think a lot of it has to do with the tip-type. MAPP gas is usually used with a large swirl-type tip. A/O usually involves a far smaller tip diameter, so the heat available is concentrated in a single small area.
A/O with a normal brazing tip is too hot and concentrated for sweating copper pipe. I think you could probably get by with a rosebud type tip OK.
Most professional plumbers I've seen have some sort of rig with a heating tip attached to a hose (or hoses). Uses the same sort of "turbo" swirling tip you see on MAPP gas torches. I think this is primarily for access (lot smaller than a nozzle on a tall MAPP canister), and probably what the hose is attached to has a lot higher volume - less stuff to lug around.
Seems to me I also read something about MAPP being phased out and replaced by something else. Don't know if the "something else" is compatible with MAPP nozzles.
Here's an article that is a review a Bernzomatic MAP-pro (the replacement for MAPP gas) torch kit. Bernzomatic is the manufacturer of the piezo-electric torch nozzle I use and love.
http://www.protoolreviews.com/reviews/plumbing/bernzomatic-bz9400qfk-quickfire-hand-torch
The new MAP-pro tanks are short and squat, where propane/MAPP tanks are tall and thin. It looks to provide a far more stable base - my MAPP torch is very tippy with the spark-lit tip on it. Of course, this may also be a marketing ploy - I don't know if the tank holds as much gas as the older style - it may be more expensive to use.
It's odd that according to most of what I've googled, MAPP is only about 200f hotter than propane. First-hand experience tells me propane is nearly impossible with 1/2" copper and I have no idea if you could ever get 3/4" copper to sweat with propane - I wouldn't even want to try.