When L.e took the bed and other items, they may not have determined the progress into the house of the perp as yet. May have noticed something odd about it, or it tested positive for body fluids. So they took it. A lot of stuff is taken from crime scenes that turns out to have no value, just like items collected during searches.
By the time LE announced they believed Jayme to be home during the crimes, they would have ruled out her being anyplace else. How many places could a 13-yr old be in the middle of the night, without someone still alive knowing about it? They surely knew by the next day that she could not have been anywhere else. Thus, that was at least part of their conclusion, imo.