First off, they're assuming that ALL tire shine products contain some sort of petroleum distillate. Not true. But petroleum distillates and silicones are the two most misunderstood and maligned ingredients in the world. Neither is going to hurt your tires, dash, vinyl & rubber trim, etc provided you select a product from a well known manufacturer. Meguiar's, Mother's, Eagle One, Pinnacle, and even Armor All (plus many more) all make products with low shine, high shine or medium shine finishes. Some are water based, some are solvent based, but neither will harm anything. No such thing as a "silicone based" dressing, either, although most water based dressing contain some silicone.
Specifically with regard to tires, any browning of the sidewall is a function of the anti-ozonant material used during the manufacturing process. This component is designed to leech out through the sidewall to prevent the tire from damage due to UV exposure. But these components only leech out when the tire is moving and under load, which is why you see RV owners always covering their tires, and why in the RV industry tires are recommended to be replaced after a certain time period, regardless of mileage. Many large RVs sit stationary for very long periods of time so the anti-ozonants don't do their job properly.
It's also a common misconception that tire dressing cause browning of the side wall, and that's not true either. The browning (technically, blooming) is caused by these anti-ozonants doing their job and you trying to clean any residue from the surface. Any all purpose cleaner will reveal this blooming, and the level of blooming varies from tire to tire, with high mileage tires producing more blooming effect than tires rated for lower mileage (usually high performance tires). Applying a tire dressing that contains some cleaners, and failing to properly clean the side wall first, will also reveal the blooming. In fact, if your side wall is already starting to crack, the cracks can become more visible after applying a tire dressing, but the dressing itself won't cause the cracking.
Overall though, the terms "petroleum distillate" and "silicone" actually encompass a very wide variety of material with very different properties. Depending on the degree of distillation a petroleum distillate can be an extremely powerful solvent or it can be food grade. Yes, you can safely eat some petroleum distillates, and people have been rubbing them on babies bottoms for decades. I like to use the analogy of plants: just because poison ivy is a plant and you would never eat poison ivy, that doesn't mean you should never eat plants or that all plants are bad. Some plants are good to eat (downright healthy even), some not so good (I have a very strong aversion to Brussels sprouts), some only have parts that are good (you'd eat an apple but not the bark of the apple tree, right?) and others will kill you fairly quickly.
