Truth equals "undeniable fact."
Well, here's the problem. Just like we don't agree on the definition of "truth" we also disagree on "deniable". From the YEC stand point, anything that doesn't appear directly in the Bible is "deniable". All you have to do is say, "I deny that".
So, for example, gravity is not true, nor asprin, nor airplanes. All of these are easily "deniable".
The question needs to be, is the person who's making such a claim basing it on rational reasoning, or strictly on belief.
I understood DNA tests to have determined that we share many similarities and differences with the great apes...not that we and they evolved from a common ancestor.
There are multiple type of DNA tests. What he's refering to is mitochondrial DNA. Unlike normal DNA which mixes during sexual reproduction (ie I have my Mom's eyes and my Dad's hair), mitochondrial DNA passes directly from your mother to you - essentially as a clone.
Because of the way it transfers, it's rate of change is very slow. So, by compairing the differences in mDNA between various groups we can figure out when various groups slit off. (for example - if the Aboriginies have something in common with the Polyneasians, but no other group has that same mutation, then we can deduce that the Aboriginies and the Polyneasians are more closely related to each other than to other groups.)
Similiarly, we can look at the full range of mDNA mutations, estimate the time it would take for those mutations to have occured and work our way backwards to a single source.
That's how we come to "Mitochondrial Eve", the single progenitor of the rest of humanity.
Was "M Eve" a homo sapiens? No. But her offspring were the ones to survive, spread out and evolve.
**Important**
mDNA is how we locate mankinds common ancestor, not all creatures common ancestor. Two different methodologies.
As for locating a common ancestor of all mammals, or all animals, or all life - we look at the morphology of the fossil record.
We look at a broad group, "Kingdom Animalia, Phylum Chordata" - which includes all animals with spinal chords - lizards, snakes, mice, bats, kangaroos, whales, people. What's the oldest fossil that has a spinal cord? What's the simpliest fossil that has a spinal cord? Where do we find just one animal with a spinal cord and no others?
If you look at a group of fossils and there are twenty different creatures with spinal cords, obviously you need to go back further. If you look at a lay and there's a lot of shellfish and nothing with a spinal cord, you've gone too far.