Acetone, though polar, is not so very polar that it will not dissolve nonpolar substances like fats and varnishes (it is often sold as nail-varnish remover). Other polar organic substances such as ethanol and ethyl acetate behave similarly. Only solvents of extreme polarity and hydrogen-bonding ability, such as water and HF, fail to dissolve non-polar substances.
SnI4 though nonpolar can dissolve both in non-polar solvents and highly polar ones like water; in the latter case indeed the polar solvent adds to the Sn co-ordination sphere, as hmx9123 points out. Many nonpolar halides capable of higher co-ordination will dissolve in polar solvents, eg BF3, TiCl4, SnCl4 and in the case of water they often are completely decomposed e.g. TiCl4 + 2H2O ---> TiO2 + 4HCl.