"Never underestimate the [insert characteristic here] of 'dogbrains' " (one word).
I caught that NG docu. I won't even try to explain it except to say that there is a tendancy for humans to anthropomorphize almost everything their pets do, even when there is little/no evidence to support it.
Our first dog (together) was a border collie mix who had a similar toy arranging behavior (though not nearly as complex/involved). Her big thing was "arranging" a new rawhide. First, she'd carry it around to show it off to everyone that it was new, it was hers, and she had it. Then she'd spend an hour
moving it from one place to another - not hiding it; it was always in plain sight - but more like trying to find where it looked best or the best place to keep it? We never knew, but it was a stitch watching her. Sometimes she even expressed a bit of anxiety as if she couldn't find the right place or get something right and was frustrated.
Our current fella does something similar with any new toy. He tries it from place to place in different positions, sometimes balancing it on the rung of a table or chair, on the corner of a table, inside my shoe or boot.... And with things that I
would have a difficult time balancing/placing where he puts them. We've found dog toys in some pretty bizarre and inexplicable places (including the bottom shelf of the refrigerator).
We don't question anymore (though we often wonder) - we just enjoy the show.