I already solved this problem, but I'm posting it here for future reference.
- You have two (or more) VMware vCenter servers in linked mode.
- You have the same permissions on all of them.
- You are not a local Administrator on the server themselves.
- You can successfully connect to each one of the vCenter servers using the vSphere Client.
- When you connect to a vCenter server, you get an error about an authentication failure connecting to the other linked one(s), and you can't access it/them in the client.
- This happens when connecting to any one of the linked vCenter servers: you can only access the one you're connected to, not the other linked one(s).