I can’t log-in to the Veloce website (https://www.velocelounges.com), as I don’t have one of these cards right now. However, if a lounge is listed, you should be able to access it just with your credit card (But I’ve never tried). I have heard that some lounges have been blanking-out
Priority Pass is a separate, competing programme to Veloce (included as part of the American Express Platinum card package, FWIW). You don’t get a Priority Pass card with the ANZ Black cards, so I believe the receptionist was in error, or that “Something’s gone wrong” with Veloce’s relationship with that lounge. I’d try whining to Veloce and the ANZ Black concierge and see if this gets you some oil.
17. Complimentary access to participating airport lounges is available to eligible ANZ Rewards Black and ANZ Frequent Flyer Black cardholders. Participating airport lounges can be found on velocelounges.com and are subject to change. To gain complimentary access, eligible cardholders must present their credit card and a current flight boarding pass in the same name at the participating lounge. For terms & conditions refer to the Complimentary Airport Lounge Access Program Terms and Conditions (pdf 63kb).
I checked with my ANZ Black on veloce and it lists Swissport Lounge in London at least as one you can access as a Black cardholder.