Permissions for sys.database_mirroring in SQL Server
The comment: "To see non-NULL values on a mirror database, you must be a member of the sysadmin fixed server role" is found in the discussion of sys.database_mirroring dynamic management view at:

https://msdn.microsoft.com/en-us/library/ms178655.aspx

Try running the following statement:

select * from sys.database_mirroring 


Using my sysadmin account, I get a row for every database. Most rows are all NULL because they are not mirrored databases, but the two mirrors report their status. If you only want to check running mirrors you could use:

select * from sys.database_mirroring 
where mirroring_guid is not null


Using my non-sysadmin account, I get nothing. No rows returned, no ROWCOUNT, et cetera, just a delayed 'ding' sound. 

So, that note is just trying to tell you not to be surprised when you get no information back. (Except, perhaps, a 'ding' sound.)