Musing on whether this is a decent rule/ house rule.
As far as I can tell - a story Asset, like an Ally, uses up a slot when it first appears as part of the story flow. Once added to deck for later scenarios it of course should behave like a normal card. However I could see a justification for house ruling that the first time it crops up and a player gains control, that it allows you to exceed any slots if you already have it filled as much for narrative as anything.
Eg the new Ally is cajoled into joining your party, and it seems to be a bit rude to summarily dismiss Luca as no longer worthy and left behind.