I'm not sure either RB's previous statement or Butch's refutes what I said.
In both examples, even people trained to hear the difference, and listening carefully for the effect, sometimes can't hear a difference in small amounts of delay. And a singer using IEMs, while being able to notice very small amounts of delay, is not what I would consider your typical listener.
Yes, I agree that it's always dangerous to make a blanket statement about ANYTHING, and qualifiers should be used when doing so. The article I read years ago might have included qualifiers, but I don't recall them.
The bigger point (not "nit picking" here ) is that when you have a vocal mic picking up a guitar amp or a drum kit, or a violin mic picking up the French horns, you're going to get latencies between what the violin mic is picking up and what the French horn mic is picking up, and you're going to have phase distortion because of it. The only way to avoid it is to perform and record in a completely unnatural environment like an anechoic chamber. Small amounts of latency, phasing, (unwanted) reverb, etc are all things we encounter everyday and consider normal to our environment, and our brains probably need to orient ourselves in our surroundings. It would be an interesting experiment to test people in which they're subjected to NONE of those phenomena for a given period of time. Can you imagine what a person's life would be like if he or she couldn't distinguish the Doppler effect, for example? Or distinguish the latency between a signal arriving in your left ear and your right ear? Similar to seeing with only one eye, I'd imagine.