If computers connect to others through the internet, the IPv6 address can reveal how many computers there are on the local network, and if certain traffic to different destinations are coming from the same computer, but also if one of the computers has gone offline but then resumes from sleep/hibernation.
To me their comment means they want to avoid that, and I agree, I want to avoid that too. To fix these, I would need to configure NAT on my router for IPv6.

Yes IPv6 address privacy extensions help somewhat, but

• computers won't use a different v6 address for every distinct destination, they will just start using a new one from time to time
• computers won't stop using the old v6 address immediately after wakeup

With v4 addresses these did not really matter, because everything was being sent from the same public IP, and and outside observer could only see what a "network" is doing collectively. But with v6 an address identifies a computer, across websites/services. Even if it's just for a "short' time, even if the address is randomized.