We do patrol the no-fly zone out of Saudi Arabia, and we've hit targets in that zone occasionally.
The southern no-fly zone is well south of Baghdad.
In the Arab world, "saying" and "doing" are two quite separate things...
Well, not publicly.
If this article is true, it describes a good strategy. Not known to many is that Clinton bombed Iraq all through the late 90's, IIRC, but there was very little attention paid to it.
I'm not defending Clinton, but I'm saying that there would be no lack of precedent for taking out various targets there thoughout the years.