No, that's wrong. You're ignoring that if it didn't happen, we wouldn't be here to see the result. Observer selection bias. The less common OoL is, the more biased our observation is.
The more subtle argument was that because life originated early on Earth, OoL must be a high probability event. But that argument implicitly assumes the probability of OoL is relatively constant with time, so it wouldn't be biased to occur early. OoL on small planetesimals is naturally biased to occur early, due to decay of those short lived radioisotopes. After the planetesimals freeze OoL there doesn't seem possible.