I think Tim did deliberately lose the musical chair task but not in the way he say's.
When he stumbled off the chair he made no attempt to recover his fall. Instead he rolled over pointlessly thus giving Alex a chance to get there first.
I don't think Tim wanted the responsibility of winning and having to choose and make himself unpopular as did Alex the week before.
They are all participants of a game so I suppose it's a valid tactic! "Maybe???
