Well, there's such a thing as similarity by convergent evolution, where in different places or times similar forces sculpt initially dissimilar life forms to outwardly similar adaptations. The classic case is Australia and Tasmania, where marsupials radiated into ecological niches we find held elsewhere by placentals. Thus there were small marsupial predators (the Tasmanian Devil), large marsupial predators (the Thylacine), a marsupial "flying squirrel," etc.
While the similarities between, say, thylacine and timber wolf can be striking, the underlying unrelatedness is also there to see. More importantly, the unrelatedness only goes so far. They still have a common ancestor way back there in time.
The less commonality the original organisms have, the more improbable any parallelism becomes. For instance, I'd be surprised if any alien lifeforms that we ever encounter use DNA for replication. All the lifeforms of earth use it, but that's generally considered a historical accident and an artifact of common descent. There figure to be other possibilities.
Woese's theory--that the archaea, bacteria, and eukaryotes evolved separately--struck me as improbable in the same way and for the same reason. (There's also the problem that the fossil record for eukaryote life doesn't go back very far at all comparted to the other two.) But there's a major difference between the Woese scenario and my alien example. Woese's life forms would still presumably have evolved from the same "ancestral" soup.
The first molecule to form a suitable basis for self-replication triggered three "abiogenesis" events, if I understand Woese correctly. It's nowhere near as big of a deal as the same parallelism would be in the alien example, where you have to believe that a different soup on a different planet did exactly the same thing as on earth.
I'd like to humbly suggest that you are still hung up on a sudden miracle that probably never did occur. Never bet long odds. There was probably a smooth transition from some radically alternative form of self-replication that was neither highly accurate, nor highly centralized, into RNA world. As has been suggested before--it is the energy conserving chemical cycles that have to start the show--and these could have formulated around such non-cellular locations as enduring paint pot bubble clusters, or smooth crystaline rock faces, to give some initial locality to beginnings of the process of enduring maintainence and replication.