There isn't much trust in Tamriel at the moment, Hammerfell hates the empire, Thalmor hate everyone, Skyrim is in civil war, invasion could come from anywhere, you wouldn't let a group of armed warriors from Hammerfell into your city just because they say there after a criminal, crime in Skyrim means your only wanted in one hold if you murder in that hold, so why would Whiterun care about a crime commited in Hammerfell if they don't care about a crime commited in Falkreath