That’s correct but I don’t see what this has to do with my comment. It’s still a fact that all modern life, at some point, came through the same individual organism (EDIT: this should be population) which, furthermore, already possessed the fundamental machinery of DNA replication, RNA transcription and protein synthesis (amongst other things).
EDIT: I misunderstood. Yes, you’re right: due to lateral gene/molecule transfer, it’s not certain that the last universal common ancestor was an individual cell, and at that time the label “individual” probably didn’t make much sense (although the paper I linked argues strongly that it was in fact one single cell).