From around the end of the second Punic War, but already to a degree by the end of the first Punic War the city's food supply was pretty much totally independent of local agriculture. Nor was Egyptian grain particularly important until the Principate. The Ptolemies occasionally sent shipments of grain at reduced price during shortages, as a diplomatic gesture, but in the Republic they were not much involved in the food supply. Even in the Principate, the three grain-producing provinces of Africa, Sardinia, and Sicily were by far the most important links in the city's food supply.

The bulk of our evidence suggests that apart from subsistence farming most agriculture in Italy for sale on the open market took the form of cash crops. Agricultural products, like all bulk goods, were expensive to ship even across relatively short distances in Italy. The most fertile areas of Italy, in the Po Valley, Apulia, Campania, etc. were simply too far away by land for commerce, and could not produce food at anything like the rate of provincial tribute. These areas continued to produce food for their own local markets, which would have been largely unaffected by the cura annonae. Italian agriculture appears largely to have moved over to cash crops by the second century or so. What evidence we have--and it's quite spotty--suggests that particularly on the ager Romanus, the only part of Italy which could reasonably be expected to provide regular supplies of crops to the city on weekly market days (nundina), cash crops, fruit, and produce had long been the primary form of agriculture. Such crops were, from an early date, more lucrative and filled the need for food other than grain, ensuring a constant market. With the exception of cash crops like oil or wine (which were also exported extensively outside of Latium) such produce could not be easily traded from further than the ager Romanus, as it would spoil. Latium was not heavily used for pasture, but in Campania especially on the ager publicus and in northern Italy there was abundant and very good pasture land. Pasture has the advantage of requiring fairly minimal oversight while providing an excellent return for one's money. From such areas of Italy would have come the city's meat supply (at least excepting pork, which can be raised without pasture), which likewise could not easily be transported except live. In a modern economy, with modern modes of transport, and modern agricultural techniques the pressures of provincial grain might have impacted the local grain trade more readily, but ancient Italian farmers had long stopped selling what was already in the third century a poor market investment.

Further, you're assuming a straight shot from field to market to consumer, which is perhaps reasonable in a modern world where airplanes can carry things worldwide within a day, but not in antiquity. In the first place, in a pre-Green Revolution world, without modern agricultural practices, the threat of famine constantly loomed. Famine hit the grain-producing provinces as readily and as unexpectedly as it hit Italy. Nor was the end of famine likely to be predictable. The result, besides the obvious real shortage of food, was generally stockpiling by distributors even in times of plenty. Even in the Principate, when such manipulation of the grain market was severely punished, sometimes there was simply no money available in the treasury for state grain--the cura annonae did not simply produce grain out of thin air, and had to deal with the distributors who moved the stuff. Such further pressures changed the availability of grain and, more importantly, its price. Market grain could vary in price rather significantly even during the Principate. The grain distributed as part of the cura annonae was by and large provincial grain, but the amount afforded to the citizen was simply not enough to feed a family, and given the high death rate in the city families must have been everywhere. Additional grain had to be purchased on the market, and the origin of that grain might have relatively little to do with its actual price.