if your body is synthesizing muscle it requires energy in excess meaning, whatever the hell your doing at the length of time during synthesizing + the energy required to build lean mass.
conversely, to lose body fat you must come in a caloric deficit, use more than you gain.
Now this only means that the body cannot do both at the same time. Unless ofcourse there was a way body fat could be used to synthesize muscle. At this moment in time, nobody knows how to do that.
This does not mean that by not being able to do both at the same time, means you cannot do both in the same day.
your body can spend 1 hour of burning fat, and then hop right into building muscle right after that depending on how your body wants to do it.
usually during physical stress though the bodies synthesis of proteins slows and the body begins using more protein as fuel as well, so this is why it's always a good idea to have a protein source in your body, a better alternative to having your body eat your own muscle.