Apparently I don't have any "good" sources on ninjas. The books I've read seemed to indicate that they did wear camo which might be black at night, or white in the snow, or whatever....but it was only for specific assignments, and in many cases, they were "invisible" by looking like the regular populace so they couldn't be distinguished from any other peasant.
But that armor was cumbersome, and difficult to use stealth with, and they tended not to wear it, unless it was specific items like a very light chainmail, or metal arm bracers or nekode used for blocking sword blows, etc...
In any case, that's what I've read. Doesn't mean it's right. I'm not a historian, nor have I taken Japanese history courses or anything of the sort.
I have a book "Art of the Ninja" by Peter Lewis, and "Warriors of Medieval Japan" by Stephen Turnbull....that's about as much as I've read about them. I'm not saying this to argue...I'm just establishing that I know I don't have a good historical knowledge of the period, and my understanding of the topic has ranged from "they were real", to "they were a complete fabrication and never existed" to "they might have been some form of special forces" and people made up stories about them to exaggerate their exploits.
Banshee
Yes, the myth about the 'black pajamas' is a Kabuki theater thing. A kabuki theater has no back stage area. The stage handlers wear those black pajama outfits so they are not well seen while moving stage sets around. While the audience can certainly see them, the intent is that they aren't really there - they are 'invisible'. The actors wear garish outfits, much more colorful than their equivalent in real world society.
In the 15th century one particular Kabuki play introduced a ninja as an assassin used against some noble lord in the story line. The actor representing the 'ninja' wore the black stage handlers suit, so as to be kept out of sight/out of mind of the audience, until the moment that he pulled the mask off his face, drew a sword and slew the noble on stage.
This was an OMG moment for the audience, for their assumption that the guy in the black suit was a stage handler and not an actor representing a ninja. This is where the black suit idea originally came from. It was not a ninja standard outfit - of course ninja were known, but little was known about them even by normal Japanese at that time.
Ever since that one play, black pajamas have been used to represent ninja in all media since then. Its a media thing, not an historic thing.
As you mentioned ninja typically dress in disguise whether as a peasant, a monk or other outfit so he can blend in with those around him while he is on mission. So a ninja should be wearing something normal.
If you were caught not on stage wearing a black stage handlers outfit, you would stand out as something that doesn't belong there, and most likely slain on sight by a samurai viewing him. If he was instead dressed as a peasant, he could say, he was lost, looking for his pet, or using the bathroom and might escape with his life.
I'm familiar with Turnbull's work, but most critics consider much of his work to be poorly researched. Some things he got right, but much was way off. There are samurai sites online that regularly consider his work as empty, and not worth relying upon.
I'm half Japanese and have studied all things Japanese for the last 30 years. I have a cousin who is a history professor at the University of Tokyo, and I regularly use him for my research. I trust my sources versus most other sources available.
Edit: Japanese never had chain-mail as an armor type. Ninja wore 'leather armor' if they wore armor at all.
GP