Large unknown corporations will likely be in their position by controlling smaller corporations. Consider how even in the real world, there are ten mega-corporations that are the source of just about everything we eat. If they're becoming powerful enough to actively wage war on each other, they probably act as an umbrella corporation over some of these ten.
Then they fake some data that gets sent to their holdings. Turns out that there's a strain of [insert generic bug like E. Coli] in the [food]! We need to recall all of the [food] shipped out to the stores in the past two weeks!
Recalls happen all the time. Nobody will really care. People pretended to care about the Chipotle health issues earlier this year, but that hasn't stopped many people from eating there. You get a temporary dip in public approval ratings, but your profits aren't affected, especially when you take on the cost of dealing with all of the disposal. The stores will ship the [food] to a disposal location, say, Abbeville, South Carolina, the corporation reimburses them for the shipment, and the [food] is then moved from the trucks into the secret base.
Alternatively: You could just ship the food to the base yourselves. Drive down an interstate highway some time, and count how many big semi-trucks you see. One time as a kid, I counted over three hundred on the road between Milwaukee and Chicago. You can pack a ton of food onto a truck and just ship it to Abbeville, and nobody will think twice of another truck on the road. If anyone asks, just say that you're testing the savings that could be gotten by building a distribution center there. Better yet, actually do build a distribution center there, so that you'll have trucks coming and leaving constantly. As long as nobody is actively measuring how much food comes in and comes out, you can say that you're holding things in storage there and they'll never know the truth.