So I ended up speaking with someone at a local VAR, and it looks like the libraries have to be downloaded manually. The current version of Solidworks PCB does not have the same integration with the Altium Vault as the last version did (but hopefully it will come back).
So for now libraries can be downloaded manually from Altium: Altium Design Content
Hope this helps someone, and I really hope the Vault integration comes back.
FYI, I just received a reply from SW tech support. To quote:
Your observation is correct SW PCB does not have access to Altium Content Vault.
SW PCB product managers intentionally moved away from the Vault to standalone libraries.
A possible workaround would be to download the libraries from the link :
But if you still feel the need, the request to include this functionality is filed in the SPR 961279 (Make Altium Content Vault available in SOLIDWORKS PCB). I am attaching the SPR to this SR.
Thank you bringing the attention about the documentation. We are working on correcting the conflicting documentation about the Altium Content Vault.
As the SPR has been created and attached, I will now close this SR. Please do not hesitate to reopen it if you have any further questions or concerns on this issue.