Many dukes do, indeed, get food shipped to them without directly paying for it. And if this transaction were to occur in a vacuum, totally devoid of context, then sure, you could say that the lord is not getting paid for it.
But then to be fair, you'd also have to look at everything that happens in the same vacuum. So when the Duke of Keplerville sends the Holy Keplerstan Army to Kepler's Fields to wipe out that monster outbreak, you can also say the the Duke is not getting anything in return. So, to be fair, maybe the Duke should hand an invoice to the Viscount of Kepler's Fields for Services Rendered.
The whole system works up and down on terms of mutual support. To say that the rural lord is getting nothing in return for sending food to the city at no cost is as much of a fallacy as saying that the duke is not paying for that food that gets sent to him at no cost. He pays for that food every time he hands gold out to a knight to recruit troops, or adds gold to the war chest, or enlarges a recruitment center, or builds a new smithy, etc., etc. All the expenses that it takes to keep the city and the realm running are to the benefit of the entire realm, not just the duke.
If the duke doesn't support the realm or his lords in whatever way they need it, then he's a crappy duke. And those lords that serve him should find themselves a new duke.
