This is true, but your actual experience/use may not show the issue.
As mains power is Alternating Current, cables carrying it give off Electromagnetic Interference.
If the EMI is strong enough, it can induce a current in the Cat6 cable, affecting the data being carried.
The Strength of the EMI is affected by how far the cables follow each other, what quality of mains cable is in use and if the Cat6 is shielded or unshielded, to name a few things.
You can reduce the effect by using a (more expensive) Shielded Cat6, rather than an unshielded one, or you can prevent it by running your cables so they don't follow your Mains power.