[grantsrc]

Not sure how you would get different intrepretations. It is stated in the rule books, but you have to do a little digging.

Players can move towards the sidelines but coaches cannot come onto the field.

9-8-2: ...During a time-out for injury, the coach and/or such attendants as may be deemed necessary by the referee may, with permission, enter to attend the injured player(s). In no other case, except as in 2-6, shall any non-player other than an entering substitute enter without the referee’s permission.

3-5-7-e: An official’s time-out occurs during a dead ball without a time-out being charged to either team: For a player who appears to be injured.

3-5-8: An authorized conference may be held during a charged time-out or an official’s time out (7h, 7l and 7m only). Only one type of conference may be used by a team during any one time-out.

Basically this means that any type of authorized conference that occurs during an injury is a foul. But it says nothing in the rule book that limits players to the middle of the field.

One thing to keep in mind, if a player leaves the field of player during an injury timeout, he cannot come back on the field. That's why it's important to keep the players on the field.