BCAAs are not what dictate whether you burn fat or muscle during fasted training. This is the same fears and myths that people have been following for years, thinking that you have to have some type of protein in your body or you go catabolic, which is nonsense. If you have that fear around cardio, what do you think happens while you are fasting, and why wouldn't you be catabolic then?
When insulin is up, your body cannot effectively burn fat. The definition of necessary is something that is needed or required. You don't need them and they unnecessarily disrupt the balance of glucagon and insulin during the fast on a day when the only goal is to burn fat.
By the way, I don't deem them that way the creator of Lean Gains deems them that way... I am not spitting out crap just read the site. The only time aminos are recommended is right before lifting in a fasted state, then every 2 hours after until you have your first meal. He never once recommends using them on a cardio or rest day, they go against the premise of the program.
Amino Acids cause an insulin release, leucine the most anabolic of them causes the largest insulin release. So insulin is still produced throughout the fasting portion of the day. It is more to do with the balance of insulin and glucagon. Glucagon is what tells your body to preserve muscle mass and burn fat for energy. Insulin and Glucagon like peptide are antagonistic hormones. Insulin is anabolic and tells the body to run off of glycogen, to store nutrients, glucagon tell the body to release fat for energy and not use the glycogen.
So...in a nutshell, consuming BCAAs before cardio will disrupt that balance, and cause an insulin release, which tells your body to burn glycogen for fuel instead of fat