You are technically correct—I did mention these checks are allowed by the agreement. But I guess what I meant by saying it "nullifies" Schengen is that it make

You are technically correct—I did mention these checks are allowed by the agreement. But I guess what I meant by saying it "nullifies" Schengen is that it makes it redundant within its own bounds. i.e. pushing minor provisions of the agreement to the point that the motivation for creating Schengen is thwarted.