The second point is not really relevant, given that the thought experiment is about our ability to detect something that was invading us. If they are invading us, then they have found us.
So you now have to explain 2 discrepancies in technology. 1) They are sufficiently advanced to have found us. 2) They are sufficiently advanced to get to us.
The more you add to the list of things they would have to have in order to invade us, the less and less likely they are missing the things required to eliminate us undetected. For example, you would have a hard time explaining how they can move their fleet across the vast void of space, but can't move a sufficient number of asteroids from an asteroid belt to populous locations on Earth's surface.
This is why I dislike most alien invasion movies.