That does seem a bit too close to just be coincidence doesn't it!
That said, I wouldnt mind of the premise for death note was inspired by something previously written. What I love about Death Note is not necessarily the basis of the storyline (there is a notebook which kills people), but the fact that the character development and plot is carried out so well. The rivalry and tactics between L and Light was so well thought out and really kept you glued to the screen (I'm of course referring to the anime here, haven't had the pleasure of reading the manga yet!).
I see the comparison here is quite in parallel with the comparison of La Jetée and 12 Monkeys.
I don't know if any of you have seen 12 Monkeys, but in the special features on the DVD they say that the premise for 12 Monkeys was an experimental french film called La Jetée, which was about a post-apocalyptic world and time travel (in a very broad sense) and 12 Monkeys based its foundations and plot on this premise. But obviously 12 Monkeys did so much more, it looked at the relationship between Brad Pitt and Bruce Willis, the complications of time travel, added lots of twists and gave you a really immersive storyline. In this case, while it's base plot was essentially taken from La Jetée, it became something completely different after Terry Gilliam developed it.
I believe that the same has happened here. The base plot of Miraculous Notebook has been taken and used as a template for Death Note, but Tsugumi Ohba has developed it into something completely different.
Sorry, I always go off into long ramblings once I get into a discussion!