Except that is slightly wrong.
Sure, they all share the same anycast IP address, but they also all need to be uniquely addressable too (at the very lease for management purposes). Otherwise how does an anycast server perform any kind of look up to an external server and guarantee that it will get the response back?
If an anycast DNS resolver sent out a request to resolve an IP from an authoritative server on the other side of the country and soured it from its anycast address, how does that authoritative DNS server know that it shouldnt just send the response to its nearest anycast neighbor?
As long as an individual providers anycast servers are sufficiently dense then you probably cant beat them for location correctness.