I suppose it's possible, but the fact that it is, in fact, DNA is enough to suggest it's from the last universal common ancestor (LUCA). If it shares the same ultra-conserved ribosomal etc sequences, then it's even more likely from LUCA.
Uniform dispersion would suggest some territoriality aspect of the species, and clumped dispersion would suggest a heterogeneity of resources (or any other hypothesis that could then be tested).