Seems like you are desperate.
It was not a spur of the moment.
DW's trip was planned ahead of time. He ended up gettting bored with the PLANNED part of his trip, and picked up camp, and headed off to other places to see if he could find his friends, or other interest. THAT PART of it was the SPUR OF THE MOMENT he was talking about.
That is one interpretation.
I totally disagree with your tone that that is the only interpretation. DW may have been deceptive about this to the police. Why not tell them your story instead of telling them just "it was spur of the moment".
No need to get to mad when people don't agree with what you think of the evidence.