I love those instructions, they'll provide a good laugh for the hard-working IRS clerks in the mail room.
The Austin Service Center, for example, is 456,000 square feet. That's ten acres. The returns will be separated and marked up before they get to one of several dozen examiners, whose cases are assigned based on various criteria. They won't be in the same batch and they will be worked when they are worked. If Mary is on leave this week, her "Open Me First" return will be processed long after Joe's "Take Your Time On This One" return.
File a paper return for the parents, claiming the kids. Just because IRS won't accept it electronically, doesn't mean they won't reject it on paper. They'll probably allow the dependent but send a letter to the parents, and to the kid, saying "don't do that again." If they disallow the dependent, you can amend then.