Contact groups cannot be created/added to even when signed in
When using third-party account types (I haven't tested with the built-in "corporate" account type), contact groups from the server are synced to the device, but groups cannot be created from the device, nor can contacts be placed in existing groups from the device. The People application says "To create groups you need an account.", despite already being logged into one.
Using a couple test devices, I found that this error is also present in some versions of Android, but not in others.