I accept the logic perfectly. Although I doubt Palpatine had much to directly do with the assassination anyway- because he knew, obviously, that Padme used decoys! No assassin under his control would have blown up the wrong person. Tyrannus was running that operation and it was deputised down on many levels. Palpatine had little reason to kill Amidala as presented in the film- Dooku only wanted to do it as a sop to the Trade Federation, and I think Palpatine does not micro-manage.
However, regardless of all that... my point is not that it makes no sense, but that I think it would have been better dramatically if Anakin had had to be performing his mission as well in that segment of the film. As in, I think the film would have been better if the threats to her life had continued! Just my opinion though.