@fiorite- Besides carbon isotope ratios, the planet earth has other buried secrets that support the snowball theory. The formation of banded iron striations in rock that is billions of years old, suggest that there was a lack of oxygen exchange between the oceans and the atmosphere. Iron precipitates out of the oceans, and the fact that the banded iron formations are not oxidized means that the water it precipitated out of was not heavily oxygenated. This suggests that the ocean was covered with something (like a sheet of ice) that did not allow oxygen exchange.
Other geologic clues include the presence of glacial deposits and formations at low latitudes. Things like dropstones, glacial till, and glacial striations in the tropics suggest heavy sheets of snow and ice once covered them. The verdict is still out on the snowball earth theory, but some of the evidence is supportive of the theory.