That's not really how the WPA rule reads:... Reminds me when a foul is called on a player for letting go of their cue while laying it on the table during their turn - it’s the rule although you rarely see it called.
6.12 Cue Stick on the Table
If the shooter uses his cue stick in order to align a shot by placing it on the table without having a hand on the stick, it is a foul.
From what it says, I'd say it would not be a foul to place the cue on the table, for example, to tie your shoes or during a timeout, providing it is clear that you aren't also trying "to align a shot."