A little googling revealed the original source of the quotation as GM Rashid Ziatdinov:
http://www.jeremysilman.com/chess_instruction/Ziatdinov_Pt_5.html
The context is on how to play better blitz chess. So perhaps the author means that unpredictable, seemingly illogical moves can be strong, particularly when playing blitz.
I stand by my original, though somewhat facetious position that logic and common sense are not integral to chess, other than the dull truism that it is logical and sensible to make the best move. Planning, calculation ability, and pattern recognition will win you far more games than all the "common sense" in the world. Is anyone really willing to defend the claim that Bobby Fischer is a beacon of common sense?
By the way, Ziatdinov also suggests that "the move of your hand must be faster than your thoughts," which is equally interesting and suspicious advice!