Some aspects of this question have been covered previously. In my previous answer, I pointed out that using octane that is too low will lead to retarded timing and higher emissions.
With respect to fuel economy, you can never trust someone's casual anecdote about fuel economy. As Mark points out, they're almost certainly going to be operating under a case of serious confirmation bias. Fuel economy is something that has to be measured scientifically to establish that, under the same conditions with the same vehicle, fuel X is better than fuel Y by this amount, thereby saving you a net of Z dollars over time T.
If the person you're talking to can't quote values for all of those variables, you're just having a cocktail party conversation. Don't take it to seriously.
In short, octane that is too low is bad. Octane that is too high is possibly a waste.
My favorite fuel economy example continues to be the episode of Top Gear where Jeremy Clarkson clearly demonstrates that a BMW M3 is more fuel efficient than a Toyota Prius. There's no question: both cars drove the same course at the same speed over the same distance and the Prius used more gas.
Admittedly, he was driving around a race track and the Prius was going "flat out" (sarcasm quotes for the Prius) while the M3 was just loping along.