He uses the same argument as Aubrey de Grey but reaches the opposite conclusion.
If aging is caused by the accumulation of mutations and 'wear and tear' then we can control it. All we need are properly placed stem cells derived from your 'unmutated' cells and taking care of the damage caused by our metabolism.
I mean: we have 37+ trillion cells in our body. To find a lot of them that haven't suffered any mutation shouldn't be hard. We could even take a billion cells and use the most common base for a given position - in the end it should lead to your original dna because each cell would have base mutations in random areas.
Or we could freeze a sample of DNA when we are young to ensure we have a non-mutated cell-line available for therapy.