JohnnyE, here's my take...
Back when taekwondo was being developed, North Korea was a communist country (and of course still is), and South Korea was a dictatorship. Of course later, in the late 1980s, South Korea became the modern democracy that we all know and love today.
General Choi (the father of taekwondo, and specifically the father of ITF/Chang Hon taekwondo) wanted to promoted taekwondo worldwide, and for that he needed funding and support, which he actively sought from all quarters. When Choi fell out-of-favor with the South Korean dictatorship, he sought funding and support elsewhere, including from North Korea. Remember that this is all happening during the Cold War, when being called "communist" was akin to today being called "terrorist" - there was nothing worse than being a commie-lover. I think that -- not only did Choi seek funding and support from North Korea -- he also wanted to promote taekwondo in all countries of the world, including North Korea. But back then...you simply couldn't do that without being branded a commie-lover. I suspect that Choi also viewed the promotion of taekwondo in the North as a way to maybe bring the two countries a little bit closer together, which is something that Koreans of his generation very much wanted.*
So no...ITF/Chang Hon taekwondo is not North Korean, but in some people's minds it is associated with North Korea because General Choi sought funding and support from North Korea and tried to promote taekwondo in North Korea.
If you want more detail, you can read here:
Timeline of Taekwondo - Taekwondo Wiki and here:
Taekwondo History - Taekwondo Wiki
* Recent polls suggest that the younger generations of South Koreans are less interested in reunification with the North. The economic toll on the South for reunification would be hefty, and the two cultures have grown very much apart in the last few decades.
** And yes, WTF-style taekwondo is more correctly referred to as Kukkiwon-style, the style defined by the Kukkiwon that is practiced by the WTF...so a lot of people incorrectly call it WTF-style...but honestly, more people are likely to know what you're talking about if you call it WTF-style, since it's better known by that (incorrect) name. You can read more about that here:
WTF Taekwondo - Taekwondo Wiki