Meh - I've been tig welding and silver soldering guns for 20 years. I understand what you are saying. But the method you described is known as "piss poor welding". Without the substrate going molten, there will be a flaw at the juncture. You're not laying the filler on top of the substrate, you are mixing them. That's the whole point of the puddle.
I agree that often there is a good question on whether silver soldering or tig welding is most appropriate. I use both techniques almost every day. And there are a variety of factors that motivate me to pick one over the other. But the temperature localization of a #00 tip on an oxy/acetylene torch is far different than some bubba with a can of MAPP gas. For that, yeah - the whole area is heated. But I assumed we were comparing two professional ly executed techniques. While not quite as localized because it takes longer for me to reach 1200 with a #00 o/a, then to reach 2200+ @ 75 amps on my tig, it remains twice the temp. And the o/a has a significantly lower temp even a few millimeters away from the solder point.
Remember, prior to WWI, welding was not an option - all gun parts requiring that type of connection, were silver soldered.