Skyrim talk:Black-Briar Meadery
"Completing Under the Table for Wilhelm makes low-level items freely available, including barrels of bottles of Black-Briar mead." - not the only way to make low level items unowned.
Other possible methods (all unconfirmed):
Passing a speech check - persuade barkeeper to "stop hiding the truth" regarding how he feels about working for his employer.
Finishing Thieves Guild questline.
Improve Maven Black Briar's disposition towards player.