Death Note Theory: Did Near use the Death Note?

I've heard this theory for a while. In the Manga, Matsuda even at the end suspected Near used it because Mikimi died 10 days later in prison from a suicide. But lets examine the theory.

1.Remember Light said Near had to have the meeting what was it over 5 days from the time they talked? At that exact time? And remember that Giovanni touched the notebook in that one scene, then they replaced it before hand? Its possible the first time they got it, Near used the death note to tamper with Mikimis movements.
2.Mikimis death in the anime was mad weird, just stabbed himself then died. Same with Manga. Does not seem like a complete coincidence he dies SHORTLY after the exact time they met.

I don't think he did, since Near has a even more negative view of the DN/Kira then L even stating in the Manga something like "If you had used it once and continued to do so after, with these consequences you are truly evil" but it is possible since again his goal was no matter what to defeat Kira.

I think he used it. Makes sense considering how he out smarted mikami even with mikami supposedly checking the death note every single day yet not noticing its a completely different book.