yes, they do; the assignements may not be by 'team', but many of the referees are still associated with teams and have 'friends' they might officiate at various events. (the most recent accusations of 'giving-love' against Boogie on smacktalk serve as examples)
refs don't stop the game in hockey? excuse me? soccer does get stopped as well, but not in the conventional sense - and you can't use a special case to make the point either, as it is clear from the vast majority of other examples that stopping play is a necessary component of a 'sport'.
from FIFA: "A dropped ball is a way of restarting the match after a temporary stoppage that becomes necessary, while the ball is in play, for any reason not mentioned elsewhere in the Laws of the Game." (highlighting mine)
"A dropped ball to restart the match after play has been temporarily stopped inside the goal area takes place on the goal area line parallel to the goal line at the point nearest to where the ball was located when play was stopped."
"Allowance is made in either period for all time lost through:
substitution(s);
assessment of injury to players;
removal of injured players from the field of play for treatment;
wasting time;
any other cause." (one wonders why time has to be added to the match if it were not 'lost' during the match...)
"If a penalty kick has to be taken or retaken, the duration of either half is extended until the penalty kick is completed."
Soccer handles game stops differently - by extending the game time (something emminently adaptable to X-Ball) but it serves the same function as 'stopping the clock' - time has stood still during the infraction and is appended to the back-end of the period.
A similar method is applied by NASCAR in the form of the yellow flag; instead of stopping the clock, time stands still. I only raise NASCAR because that's the other favorite argument by people who have not really delved into the matter.
Control of game time is essential to any sport, and some form of game stoppage is essential to the application and enforcement of the rules.
This can take the form of 'timeless' games (no clock is running so there is plenty of time to 'pause' and adjust things), turn-based games (following, and even during, each turn or portion of a turn there is an opportunity to halt and adjust), and every other form.
A perfect example of the importance of time control is the simple game of hide-and-go-seek: every child is keen to listen to the seeker's countdown and jumps immediately on short counts as being 'cheating'. There's no official rules, no referees, no money at stake, but the player's naturally recognize the importance of the time component as being required for the fair completion of the game. Short-counters are forced to 'do-over' until they get it right. In fact, the game is impossible to play if the 'proper' (admittedly variable) amount of time is not assigned to the countdown.
Somehow, I'm reminded of the word 'contrarian'...