Nucleotide frequencies in Kimura's two-parameter model
If sufficient time has elapsed, there will be a large number of transversions present between the original base and the final state. The initial state will therefore not matter.

Say, you flip (turn over, not toss) a coin at random intervals. For short time and few flips, the initial state will matter. But if you go on flipping it for millenia, the final state will be essentially random -- you will not be able to tell what was there in the beginning.