Right - I don't see how they can make this workable either way. If a pitcher can be put into the next game after being taken out before 3 batters for "injury," pitchers and teams will just fake injuries all the time or at least be way oversensitive to any minor pains that they can label an "injury" (by August if not earlier I am sure all relief pitchers have minor aches and pains they are dealing with).
If a pitcher taken out for injury has to then be removed from the active roster (or otherwise prevented from pitching) for a certain number of days, however, that will almost certainly lead to MORE injuries to good relievers because teams and, likely, the pitchers themselves will be reluctant to declare an "injury" during their appearance, especially if a big series is coming up, the bullpen is already depleted, etc. It's not going to take long before a good pitcher feels a tweak in a joint that, in the absence of this rule, would result in his being taken out of a game but where the pitcher instead tries to grit it out only to aggravate the pain and actually be rendered injured for a longer period of time.