My doubts are simply because he deleted the texts, there are the discrepancies between what he says and what his colleagues and manager say and also the doubts about being asleep in bed with headphones or being on the sofa. In a completly truthful statement there is no place for these doubts as all has to be right and no discrepancies can be found.
I think it's unwise to place too much importance on these discrepancies. The work colleagues had no reason to pay close attention to what DD said at this time. I wouldn't remember the exact words used in a casual conversation several weeks later. Their statements were made through the lens of knowledge that a young girl had been killed and dismembered. Now quite possibly they have good memories and have given verbatim accounts, but equally possibly they are coloured by hindsight and the desire to help bring the culprit(s) to justice.
And it's perfectly possible to be truthful, but still get details wrong because we forget things or mix them up.