Yeah, an organic solvent on an organic compound doesn't sound like a great mix. I'm sure the efficacy on logo removal is top notch, though I have no idea the extent of the damage to the underlying rubber. It really depends on the rubber compound and the condition of the tires.

If you asked any tire manufacturer in the world, they would say "don't." But in the real world, worse things have transpired with little negative results.

Again, it's a strong organic solvent and your tire is an organic compound.

Source: I am an industrial chemist.