I've trained in several martial arts (krav maga, muay thai, Brazilian jiu-jitsu, jeet kune do, kali) over a time period of eight or so years. For all their differences, they – and all martial arts – have one thing in common: partner training. There is no martial art where partner training doesn't play a crucial role. So like it or not, you are going to have a major impact on the quality of training your partners get.
Now, suppose someone, particularly someone for whom English is not a native language, hears me say, "Ehh, howzit?" to a friend and decides it is the way a reasonably well-educated, upper-middle-class person greets others. After all, they heard me say it, and I make my living using words. Therefore, it must be correct.