The Hooked start is in a Japanese kendama instruction book. That's about as legit as you can get.
I imagine two 13-year olds playing each other at K.E.N. One sets Lunar with the twist start, the other one matches it with the hooked start. The first one, thinking he was about to win, says "Hey, that's cheating!".
Complete and utter conjecture, but I'm sure it was something as silly as that that started the "cheating" misinformation.
If you are entering a (serious/proper) competition though, it's always good to check - just in case.
The Japanese book is where I first saw it. I've always just thought of it more as two separate tricks. For your example of the K.E.N. game, if one person sets the trick as 'pull up lunar', the other must also perform a pull up lunar.
How you get into a trick is often as important as the trick - pull up lunar and spacewalk to lunar are obviously different tricks, even though they both end in the same position. Of course, pull up vs. hanging is a smaller difference, but it is still there.
Just my two cents, in reality a lot of people interchange pull up and hanging starts. When in doubt just ask the people you're playing with what they think, so that everyone is on the same page and there aren't any misunderstandings! Kendama is supposed to just be fun, right?