Err, no no. The shtick with muscle tissue is that there are constantly two processes at work - one that makes muscle tissue, and one that tears it down. Both are always active. The "input" for the "make muscle" process is amino acids, and the higher the blood amino acid count, the faster that process works. Yes, that process requires ATP, but not really very much ATP, in comparison to say, actually using the muscle.

The work is being done (well, encouraged... it's actually being done by complicated enzyme reactions and such, the details of which you do not want to know) by the "make muscle fast" hormones, and those hormones are increased in quantity by exercise.

And "fat burn" is slower than the cardio because faster energy consumption chews up glycogen storage faster. Remember, the preferential order for energy sources is glucose, followed by amino acids, followed by fatty acids. All three are being consumed simultaneously when energy is required... and a slower total energy consumption rate results in a higher proportion of the energy coming from fatty acids.

This is because when you pump up the rate at which energy is consumed, it comes easiest to increase the rate of glucose burn, followed by the rate of amino acid burn.

Seriously, if you want to burn fat, take up fidgeting. Constantly. All the time. Twitch your feet all day long. Guarantee you, you'll burn fat.