I'm pretty sure that this originated on
standardized tests, like the
SAT,
ACT,
MCAT, and
GRE.
The reason for this is that there are sections of the test that you can complete only one at a time, and you can't go to other sections until everyone is ready. Since the paper is so thin and flimsy, you can read the lettering on the other side.
The point being, once you got to the last page of the section, you could have read through the page to the next questions, getting an unfair start. The other side being blank helps prevent cheating. The instructions and questions begin on the page after.
Why announce it? Simple. Some people immediately assume that their test sheet is defective, and can complain that their score should be invalid. The disclaimer is there to avoid a simple mistake that could happen the first time. Of course, high school students take dozens of SATs and ACTs, so they don't even bother reading it now.