I'm still on the fence about this. I understand what you're saying, but I still believe that would fall under the guise of rumination or an obsessive thought.
Here is a paper from the Industrial Psychiatry Journal that backs up my claim. Of course this is a bit dated so maybe the definition has changed. But my understanding is that delusion = A thought that no matter how contradictory to reality, is believed fully vs. something such as a ruminating thought or an obessesive or intrusive thought = A thought that is brought up frequently and causes anxiety. In OCD, patients can recognize their thoughts are irrational, but because of the anxiety they cause, they still have to follow them.
Your example, thinking the neighbor is a serial killer because of a leaking trash bag, could go both ways. On one hand, the person could believe that whole heartedly and have no doubt the neighbor is a serial killer, that would be a delusion. If the person thinks the neighbor is a serial killer, but is on the fence about it (Understand that the thought is silly, as you put it), I'd say that this would fall under an anxious or maybe even intrusive thought. It causes the person anxiety, maybe even severe, but if they know that it's probably irrational, then I wouldn't consider it paranoia.
But still, I'm not an expert by any means. Just some guy with an interest in psychiatry. Feel free to tell me what you think. I'd love to hear it, because this is stuff I've always just spit-balled on and never got to really discuss.
Edit: A word.