This is absolutely true. I have had several experiences of knowing music was live at a distance of several hundred feet, through nothing but how it sounded. And like you said, it's easy to tell primarily with "analog" instruments like brass, accoustic stringed, woodwind, drums, etc. Basically anything where the sound comes from the vibration of something besides a speaker.

Come to think of it, maybe that's why? Maybe the intrinsic harmonics of speakers cause overtones different than the material of the instrument? Or, similarly, maybe the material of the recording microphone changes the harmonics levels compared to the human ear?