Its just typical chinese nationalist mythology. 'We all speak the same language' is just another fairy tale they drill into their heads, along with '5000 years of culture'
When youve talked to one of them youve talked to all of them.
A few dialects are unintelligible indeed, and they're mostly spoken in southern parts of China. But most people can understand dialects spoken in central and east (north of Changjiang river) fairly easily even though they cannot speak those dialects.
When youve talked to one of them youve talked to all of them.