the west bank, on the other hand, is considered to be "judaea and samaria", which is actually at the core of historical israel. hence the colonization through settlers. so long as israel is a "jewish state", it will never cede it's claim to the west bank.
it follows that they can't accept a unity government, because they fully intend to exterminate the palestinians from the west bank (perhaps by deporting many of them to gaza...), whereas they really don't want sovereignty over gaza. to israel, these are separate areas with very different futures, and they will do whatever they can to keep it that way.
it follows that they were probably less concerned about fatah influencing hamas and more concerned about hamas influencing fatah. despite the western rhetoric, the israeli perspective is that the government in gaza is legitimate and the government in ramallah is not. they consequently can't have what they see as sovereign leaders in gaza integrating with what they see as a province in the west bank, as it would give gaza rights to a territory that israel thinks it has no rights to.
the western propaganda is designed for internal consumption. it rarely has any remote connection to reality.