The significance of epigenetics is often massively overstated in popular science. I have a book here by Nessa Carey called The Epigenetic Revolution. It's interesting but I suspect it is also much exaggerated. The ridiculous headline and strapline in the Guardian is a classic example of bad science journalism.
Environment may have a passing effect on the expression of genes but the basic code is still the same. The physical folding of the DNA molecule actually affects the translation of genes.
Regardless of the long-term conclusion on the significance of epigenetics it has no bearing on the fundamental fact of common ancestry.
I think this is the third or fourth time I have made the same point. All extant species - and the 99.9% that have gone extinct - evolved from a common ancestor. That will still be true in 10,000 years time whatever details of the process have to be reconsidered.