Get-Mailbox does not reflect the correct Server name for Mailboxes on databases for a DAG

We got notified from customers, that the powershell commandlet get-mailbox in Exchange 2010 (see http://technet.microsoft.com/en-us/library/bb123685(v=exchg.141).aspx) and in Exchange 2013 (see http://technet.microsoft.com/en-us/library/bb123685(v=exchg.150).aspx) do not always return the correct ServerName  or ServerLegacyDn for the given mailbox. Those customers often rely for their backups or customized mailbox processes on the information, on which server a given mailbox is currently located….