Running and burning muscle question!

Well, the National Strength and Conditioning Association would disagree with a number of your assertions, but they are just a bunch of "dogmatic scientists", so what do they know........

Without explaining the larger meaning, using a term such as "building muscle" in the context of the initial adaptation to a new cardio exercise is misleading. I explained pretty clearly the issues involved with cardio exercise building "strength". It seem like you are using the phrase "building muscle" as though it is applicable to the same degree in all situations.

While, by strict definition, it is technically possible for an untrained person starting a cardio program to "build muscle", that does not compare, nor is it equivalent in any way to what is commonly accepted as "building muscle" through a resistance training program.

And, again, while there is an initial adaptation to the demands of doing a stairclimber, that exercise, like any exercise that primarily aerobic in nature, does not require "a significant level of strength". It requires an "adequate" level of strength that may or may not represent a significant improvement to a specific individual, based on their initial level of conditioning.

And, finally, increasing strength is not the same as increasing muscle. People can realize substantial increases in muscular strength with only modest increases in muscle mass. Someone in a calorie deficit can still continue to significantly increase strength, even if there is little or not increase in mass--at least for awhile.