I think it has been stated but softball sounds a lot different from baseball. Baseball you go until the play is over then tend the wounded. For what it is worth I like the softball way better where the ump can immediately call time if he thinks a player is injured.
For what it's worth, the high school baseball rule is pretty much identical to the high school softball and ASA rule on this point. I think that you'll find that to be the case with most amateur or youth baseball rule sets. Play is to be stopped for serious injury.
Personally...I don't think you should treat a skinned knee the same as a line drive to the head. And, like MTR said above, an umpire really needs to wait only about five seconds before calling time to get a good read on if the runners are advancing, the defense might still make a play or if everybody is just going to stop where they are. Five seconds might seem like an eternity when a player is down, but I can think of very few circumstances where waiting five seconds would have any material impact on the medical outcome of an injured player.