He quotes an old truism against unnecessarily picking fights with the media - in the saying's heyday, this being newspaper publishers, who notionally bought ink

He quotes an old truism against unnecessarily picking fights with the media - in the saying's heyday, this being newspaper publishers, who notionally bought ink by the barrel (though more likely as a concentrate), and certainly could and did slant both editorial and opinion coverage in the organs they owned. The specifically quoted figure uses ink in the (specified) large volume of a barrel as metonymous of the volume of negative coverage, accurate or otherwise, anticipated to comprise the publisher's side of the fight.