Where are the statistics to back that up? I get that he said 'the stats back him up,' but then he gave no stats. I'm not saying it's wrong, it just seems a little strange that it would be the case for a sizable number of players, and I would need to be convinced.
And while aggregate data would be interesting, in order for a comparison to be made, you're obviously picking players who have both played the field a majority of the time and then DH'd a majority of the time. And I'm guessing that for most of them, they didn't start DH'ing primarily until they became worse defenders...which is usually about the age most guys start declining offensively naturally.
Dunn, for example, who he uses there, didn't begin DH'ing much until 2011...when he was 31. So his offense certainly did drop once he began DH'ing...but it also dropped once he was past 30. So it's tough to draw significant conclusions from that.
So it would probably need to be some data gathered from players who both DH'd and played the field at similar ages. That's obviously a tough sample to draw, but it would certainly be interesting.