In all tournaments I have run and rooms I have worked in we have had the rule that no spectators are permitted on tournament tables. Players must stay at least a "table length" away, that is: the distance to the next closest empty table.
Reasons?
A) Players are generally under more pressure in a tournament environment, and I don't want any distractions.
B) If I'm at a live table and don't like that a player is spectating, I can always ask to move tables or even leave the game; I don't have that option on a tournament table.
C) If I'm the floor, I am more involved in the tournament tables, i.e. I may have to count down all-ins, move players to balance tables, break games, observe multiple side pots for accuracy, etc. I don't want any unneccesary obstacles (the spectating players) in my way.