Not having a go at anyone except maybe the TIA but I have never heard so much C**p in my life. I used to work for a chemical company that supplied many of the base products that went into tyre shine, the same company also supplied all the synthetic rubber compounds to the likes of Michelin, Pirrelli etc.
So in the construction of a tyre you have natural and synthetic rubbers, mixed with carbon black and a cocktail of chemicals, this is known as a Masterbatch. Many of the chemicals in there are petroleum or silicone derived, then after this there is extrusion and Tyre building but for this we'll concentrate on the chemistry of a tyre.
The main cause of degradation or dry rot of a tyre is UVA absorbsion the same as in modern plastics, in order to combat this UVA protection is added into the cocktail of chemicals that go into the masterbatch. As regards the comment waxes are added to prevent attack from ozone and move to the surface everytime the tyre flexes, well this might have been true 30 years ago but is not true in modern tyres unless you count Polyethylene Glycol as a wax (which some people do) but even then once reacted in the masterbatch it would stay chemically and physically locked in the matrix.
So onto the Chemistry of Tyre shine, well most of it is silicone based with non ionic surfactants and synthetic waxes, the older stuff is petroleum distillate based which is not nice to handle or use and is really outdated now and I can't really comment on its compatibility with modern tyres but there will not be much of this stuff left in existance now due to the green lobby. Anyway modern Tyre shine and I'll talk about one paticular brand " Tyre Slik" (but they are all variations on a theme). These products are specifcally designed and formulated to match modern masterbatch compounds, they are not corrosive, most are pH neutral and they actually give protection by blocking the UVA rays that cause tyre degredation, they work in combination with the chemicals in the tyre to restore flexibility of the sidewall and inhibit cracking as well as cleaning and giving a surface resistant to traffic films and dust.
So how people can say they can impact tyre life and safety is beyond me, having had 30 years in the chemical industry and being an advanced driver trainer I would never compromise safety all my cars have always had tyre shine on and I have never had a problem, in fact I would say it's actually contributed to the tyre life, particularly on cars that dont get used a lot say just at weekends for example.
From what I've seen and know there is no issue with these products as if there were there would have beeen some action or comeback by now.
Just my 2p worth