For something to be misleading, it must mislead people. If people don't understand the "correct" usage, they can't be mislead by the "incorrect" usage.You are correct in that most people don't understand the differences. It is nonetheless still misleading, and a true watering down of meaning of words. It is wholly inappropriate and should not be done. I see it akin to false advertising!!!
I do not believe we are talking about a linguistic subtlety...like a slight nuance in meaning between words...they are completely different and have very different meanings.
I put those in quotes, because what we're talking about is a designation by the Japanese government. Words' meaning comes from usage, not commandment. The best example I can give is that many MA schools put "karate" on their signs because it communicates to the general public, though what they teach may not be (strictly speaking) karate. To some, both that usage and the "incorrect" jutsu are like putting an incorrect brand on a car - calling it a "Ford", when it's not. But those aren't actually brands, but descriptors. To me, I see nothing inappropriate in the usage, so long as they are not making false claims to students. You and I will know their usage isn't technically correct, but it's correctly descriptive to their target audience.
To me, the issue is of small importance. It's like when CRT monitors were labeled by their "size class". Monitors were typically labeled by their diagonal viewable area. Some were labeled '15" class', but were actually 15.1" or even 14.9". That was a typical usage, and didn't confuse users. In the details, the exact size was given, so there was no deceit.