First, "shinobi" seems to be the most respectful term for this group of people. Is it disrespectful to use the term "ninja"?
No, but neither term was in much use historically.
Second, in competitive situations, I have found the value of first allowing people to underestimate me (football, sparring, debating, etc), until they think that I am not a threat to them. (Sometimes allowing them to look down on me for months.) Then, when I surprise them with some skill or technique that they didn't think I was capable of, they start wondering what else I can do. Before I know it, they imagine that I have almost supernatural ability, because their own imagination runs amok. People have been told on more than one occasion that I can "Do anything". Which of course I can't. But I don't tell my competitors that.
It seems that the public vew of shinobi is like that. Either people dismiss them as nothing more than theives and assassins, or they think they can jump over 10ft walls.
Is it likely that the shinobi realized the value of underestimation that I have, and purposely set out to spread different stories to mess with their enemies minds, while making their skill highly coveted by their allies?
Wouldn't it be easy to tell people that "no, I'm not anything special -- I'm just a merchant" and then let someone see you do a magic trick and dissappear. They will spread your reputation faster than you ever could.
-But again, I don't know if that kind of thinking even has a place in the eastern mindset.- I'm from the northwest states, and that kind of thinking is relatively cultural. I went to southern Cal, for college, and they had no idea what I was doing. (BTW, it worked really well there.)
No, you are off the mark. There seems to be no attempt by the ninja to make them seem rather supernatural. That would make them a threat.
Third, if the shinobi were trying to gather information, it would make sense to appear harmless -- a farmer, a merchant, a gardener, a musician, etc. so that people will keep their guard down and share information freeley. If that's the case, a working-class person wouldn't carry either a katana or anything distincly "ninja", but a general, working class waikizashi, right? (That's assuming that the working class carried waikizashi.)
Then, if I were a shinobi, I would dress as a merchant, (even if I was a samurai) drink some saki at the local pub, and sit around and tell legends about these crazy ninja-types, while gathering information. Thus the legend will be planted, watered and nurtured, and my mission would be accomplished.
No, popular culture during the Edo period seems to be a big source for the idea that they were supernatural. You know how media exagerates things for effect. There are some cases like the death of a Shogun while in Koga from disease. He most likely died from bad sanitary conditions, but in an age where magic was thought real- there was some talk it was a spell.
Remember, the Iga and Koga regions were known areas surrounded by paranoid folks. If these warlords thought that their neighbors were hiding mystical abilities and might come after them, they would be more likely to launch an attack before that could happen. The ninja tried to not draw attention to themselves or any abilities other than gathering information. In fact- unlike Hollywood, that is about all they were really known for at the time it seams.