Your manual is stating a very wide general protection of fault to protect itself.
if you have a dinosaur based two stroke oil mixed with decent gas the oil should not separate, the gas gets stale. The gas will lose its low end boiling points,in other words the easier lighting,easier to vaporize with the air parts of the gasoline will evaporate. this could effectively lean out your jetting and cause problems but I would suspect that this would be an extreme example.
But if you use a castor based oil and or a gasoline that has alchohol in it as an oxygenate your oil can and will separate from the gas which could happen in a relatively short time.
I don't believe that the oil in itself will loose its lubricating properties as it is stated word for word but the mixture will change its properties. Whether the gas getting stale or certain oils and gas additives coming out of mixture might cause you problems that Honda doesn't want to get blamed for.