I just noticed something. So in death note the last name, L got the death note, after he watched Misa killing criminals with the death note. He then replaced her death note with a fake one. But here's the problem. L said, that they made fake news that the criminals Misa ''killed'' died, but Misa should've seen that they were still alive, because a rule in the death note states, that a person who's dead, doesn't have a name or a lifespan above their head in a picture.
Humans that have traded for the eye power of a god of death cannot see the name or life span of humans who have already passed away by looking at their photos.