Lateral (horizontal) gene transfer? Yes, that's another possibility. It
could have swamped out the ancient polyphyletic signal so that it is
undetectable today.
Assuming, of course, that the use of the same bases and amino acids and the
same genetic code had already evolved independently. You see, if I swap a
gene from _your_ mitochondria to _your_ nuclei, it simply won't work.
Vertebrate mitochondria read one of the "universal" stop codons as
tryptophan, so at every tryptophan codon in that gene there's a 50/50 chance
that your cytoplasmatic ribosomes will just refuse to continue the protein.
Swapping information between a PC and a Mac is a lot easier.