"Live" or "Acoustic" are examples of those terms which are used as either inclusive or exclusive definitions.
Those who believe in exclusive definitions will rule as outside the definition, any performance in which the slightest aspect of recorded material or sound reinforcement is present.
Those who believe in inclusiveness, will count as live any performance which is capable of being performed live, even if it was, in this particular case, not performed to a live audience. Similarly an acoustic ensemble might include some amplified instruments, or use sound reinforcement.
The difference seems to be intrinsic to the particular personality types who clash here so often. As the song says, "mostly saying hooray for our side."
Purely as a personal observation, I would count miming to a backing track onstage as a live appearance, but not as a live performance, and would not feel any reluctance to hear an acoustic act which included bass guitar or simulated acoustic piano produced by an electronic keyboard. I would also far rather hear them through a good P.A. than not be able to hear their unamplified efforts at all.
Cheers
Dave