It's an interesting approach, too bad they decide to ignore data that doesn't match their theory. And even then it's perfectly possible that life evolved/got more complex faster in the beginning before the growth of complexity got to the current model, a kind of biological inflation, akin to the cosmological inflation.
That is a really interesting idea (re: biological inflation). The only reason I would be hesitant to accept that is that biological life is still an evolutionary process and the mechanisms required to build a complex cell would have operated at slower rates than those operating in multicellular organisms. But maybe lack of competition would have allowed for a quick proliferation? Maybe when life took a hold of the light elements on the planet that process happens very quickly? We don't know! It is a big mystery! I'm sure someone will test the biological inflation idea one day. I honestly think Earth was seeded with complex replicating chemistry during the Late Heavy Bombardment 4 billion years ago. I don't think that chemistry has pre-galactic origins, but it would explain why single-celled colonies appeared on Earth as soon as they possible could have (i.e. post-Hadean).