Why did L not prevent the report of Kira's tests in the police database if he already concluded he must have had access to such information?
Probably because a public statement is different than a closed one.
Preventing these informations from leaking into medias would avoid &quot;indirect bragging&quot; from Kira (by the intermediate of the police), and avoid depreciating the police's image as well.
Then, maybe L knew that Kira would see this note, and be provoked by L contradicting his image. Since ep2, we know that Light is really aware of his image as Kira.