"You have got to be kidding me! It is not just the oil in the grease, but he additive package as well. You may have gotten away with this, but I wouldn't touch this idea with a 100 foot pole.

Also, what is the tire made of? And when the grease migrates onto the tire what will it do?"

I suspect this is severe over-reaction. Show me physical evidence of a tube being negatively affected from grease and I might, maybe might stop this practice, but until I have seen a tube failure from exposure to grease I will continue with it. FWIW I have also done this on my own motorcycle without any issues. The rear tube is now 20 years old and has yet to fail.