I disagree.
The transfer of genes betwen organisms, that Margulis refers, to is called 'lateral gene transfer'. It does indeed complicate genetic studies of early evolution; it's hard to construct trees if bits of one branch get lopped off occasionally and attached to other branches. For example a recent (pretty speculative) paper on the early evolution of the globin gene claims there is evidence of two indepedent gene transfers between unrelated bacteria in the early history of the globin gene, between one billion and two billion years ago. However, so far it appears these gene transfers, while they complicate molecular evolution studies, are not so common that they completely mixed the gene pool or prevent tracing of lineages.
Lynn Margulis, BTW, is the originator of the 'Gaia' hypothesis. The 'all life is interconnected' theme is as ideological with her as it is scientific.
RNA world, if it existed, certainly predated all this, and may not have lasted very long. In an odd analogy, and one I wouldn't want to stretch very far, I see it as similar to the inflation period of the inflationary universe - where there was rapid mutation, presumably massive generation of molecular diversity, all sorts of strange splicings and hybridizations of genes, a sort of roiling ferment of life which resulted in the evolution of the basic framework of the cell. Once the cell had started producing reduced ribonucleotides, perhaps initially for entirely different reasons, those deoxynucleotides started to be incorporated into the genome (and remember, RNA-DNA hybrids are well known), natural selection took over, and the chemistry got a lot less interesting. In fact, I see no reason why this had to be a sudden change. You could have had replacement of U by T, then C by dC, then A and G by dA and dG, in several stages. Some genes - maybe the ones where stability was most important - could have been replaced first.
So, to answer your question, 'RNA world' was probably the very earliest part of the 2 billion years of microbial ascendancy. The chemical relics of RNA world - the very ancient enzyme that produces DNA precursors from RNA precursors, and not vice versa, plus the fact that the most fundamental organelle - the ribosome - is RNA + protein, are tough to explain away with a DNA based origin of life.
I gather you consider so-called "Gaia theory" to be utterly beyond the pale, because it is "ideologically tainted" and thus not pure science. Neils Bohr perhaps (given his rigorous epistemological method) would have taken a dim view of this. But one might counter that there is a "concealed metaphysics" or implicit ideology at the heart of the Darwinist conception of evolution as well.
In any case, as I've already mentioned, I truly am grateful to you for paying attention to this discussion. Thank you!