Maybe, but a live recording doesn't sound any better than any other recording, does it?
Most live amplified performances I have heard don't sound anywhere near as good as recordings I have of the same bands playing the same music. Just the other night I went and saw a friend of mine perform live with a great band. It was an awesome performance, but the sonics were not too spectacular. His CD of the same material sounds much better, although it does not sound "live" like the show did.
I think there is a disconnect in this argument between there being cues that told you it was a live performance vs. the music actually sounding great. Just because it sounds "live" does not necessarily mean it sounds "good." You state that this band playing through these tiny speakers sounded "amazing" but I have a hard time believing that. Sounded live, yes. But amazing? Through a p.a. system? I just don't buy it.