But mankind has been using genetic engineering for thousands of years to change how plants and animals taste and increase yield. Husbandry is effectively genetic engineering where you breed out bad traits and in good ones, its created meatier, fattier cattle, plumper strawberries, corn that doesn't scatter its seed and stays on the cob getting fatter and sweeter.
I can see where altering certain genetic traits could change the taste or texture of a plant. Tomatoes for instance have been genetically altered in the last 5 years to have thicker skins so they don't bruise as easily. If I remember correctly they altered the gene that creates pectin in the fruit. Excess pectin can alter the flavor and texture of a fruit. Now there's talk of adding a gene that fish have (one that creates an antifreeze like protean) to keep tomatoes from freezing to make them more cold tolerant.
The big problem with genetically altered food is that it is more homogeneous and less likely to be able to resist blight or disease it also requires more nutrients and fertilizer to grow in the long run because of what we are engineering it to do. Why, because a lot of it comes from the same seed or group of plants. American high yield wheat is a good example, we ship its seed everywhere at a premium cost, because it yields' more seed per bushel than any other plant. African farmers like it for a season or two, but then find it cant grow in their soil (because they cant afford mechanized fertilized farming), then they find that they cant grow other crops they had been able to grow after traditional african grains. The super wheat sucked all the nutrients out of the soil.
But your right most genetic engineering would do little to change the taste of produce and meat. I would hesitate as a scientist to say that it wasn't possible.