Packaging - The Great Leak Debate

Well I don't think its a debate but I guess that's how things start!

What is your experience with pumps and tanks with horizontal agitator shafts that are installed with packing? We are in the food industry and the production and QA teams are insane about leaks, and yet most of the equipment has packing instead of mechanical seals.

In my experience and everything I was taught says packing should leak, as its a form of lubrication and the shaft is at risk of getting damaged if it doesn't. Especially those of you in the food industry, what is your experience with this? What would you consider acceptable leaks?