There is absolutely nothing wrong w/ saying "no". What she's asking is a HUGE imposition on anyone - newly married or not. Huge. It's one thing to ask "Can I stay a week or two while I find a place", but to ask to stay that long?
BUT I agree that your concerns are a bit "huh?". To waht jnjumommy said - you say you trust them, but then you say you dont' want them to be alone. That actually means you DON'T trust them.
So yeah, I think you are oddly paranoid. not wrong in wanting to say no, but your reasons/reasoning is just odd.