As someone who speaks Japanese, I will give my reason for saying why "jitsu" is wrong and not just another way of saying the same thing.
There are two main systems for writing Japanese. The national and Hepbourne system. I hate the national systems with a passion but it is taught in schools here. In that system, you write sounds like "tsu" as "tu" and a sound that would sound like "chee" in English is written "chi" or "ti" in the two systems. So in this case, either would be considered acceptable, "ninjutsu" or "ninjutu." A Japanese looking at the word and translating it back into Japanese would get it correct.
But a Japanese looking at "ninjitsu" would translate it back just like that and not as the word is originally in Japanese. That could cause some problems and has caused quite a bit of mirth in my experience. It is kind of like a Japanese trying to say "election" but writing it like they would in katakana with no difference between L and R- and that has happened before.
So for the sake of getting it correct and recognizable to a Japanese speaker, I would think you would want to differentiate between Ji and Ju as much as possible.