He was forensically aware of the evidence that could potentially link him to the murders of Maggie and Paul (Fibers, Blood, DNA, Fingerprints on Paul’s phone). He is also trying to distance himself from knowing they were already dead by offering up that he checked both of their pulses and covers himself additionally by saying he handled Paul’s phone etc… The problem with this story is that he didn’t have any blood transfer on his hands or ears or pants- which he should have if he was kneeling beside them checking their pulses and for breathing. However, it’s more important in his mind- to not have any blood on him because it would initially look suspicious that he was involved and this met the immediate needs of the offender. In an innocent unadulterated scenario, he should have some blood transfer on himself, but not blood spatter or blow-back blood.