So far as I can see, everything he's said is perfectly plausible.
Do I lock the door of the bathroom when I'm alone in the house? Frequently. It's a habit. A split-second later I think "Why did you lock the door, you twit, there's no-one here to barge in?" but at least I've broken the anal habit of instantly unlocking it again - it can wait until I've finished.
I don't know how many contributors to this thread have been awoken by a burglar. I have - albeit one who had broken into our garage and not the main part of the house. It's extremely disorientating, and I've posted elsewhere on this forum that if I'd had a firearm available I'd have shot at the bugger as I saw him climb over the garden fence. That, to me, is an excellent argument for not having a firearm in the house, because when blinded by adrenaline, disorientation and fear, the human brain is capable of reaching, and acting on, some very outlandish conclusions.
Could he have carried her body downstairs? Even with stumps, he can shuffle down on his arse, and pumped full of adrenaline, as he must have been, he would have been capable of quite a lot.
Do I believe what he's said? I neither believe nor disbelieve it. Fortunately I will never be called upon to make any decisions in this case, nor, I hope, anything similar to it.