I guess I am confused if one of the Tenets is Integrity in TKD why say something is 2000 years old when it is not, because they felt it was justify and accepted makes it OK?
The Tenets are General Choi's creation; it is only a part of his particular branch, although many have adopted it for curriculum filler purposes. The tenets, for example, are not in the Kukkiwon Textbook.
But try and read the part you quoted carefully once again, understanding that it is a translation of an article originally published in Korean for a korean speaking audience.
Chong Woo Lee’s Response]: “I am one of those who wrote that in a book. To
be frank, we did not have much to come out with. At an early stage in the course of our
introducing Taekwondo to foreign countries, when we said ‘Taekwondo was a Korean
traditional martial art’, it was well justified and accepted. However, although there was a
resemblance, it is in fact different. Should we consult [Taekwondo’s] historical origins, it
could be persuasive to say that Japan adopted their martial arts form from the Chinese
martial arts, and it flowed into Korea later. Japanese people scientifically developed
them by making many modifications from the Chinese martial arts. It seems that there
remained a problem. Japanese people put emphasis on muscle strength rather than on
flexibility in the course of developing the form of exercise. Accordingly, you cannot
avoid the body movement being stiff.”
“I am one of those who wrote that in a book." -- Many people wrote the same thing in books, including the original Kukkiwon Textbook which GM Lee was the chief editor of. He is not saying that he was the first one or the only one.
"To be frank, we did not have much to come out with. At an early stage in the course of our introducing Taekwondo to foreign countries, when we said ‘Taekwondo was a Korean traditional martial art’, it was well justified and accepted." -- At the time, "it was well justified and accepted" because the fundamental difference between Taekwondo and other martial arts was the emphasis on kicks, which comes from Korean culture. They needed something to explain korean culture, so they went back and cited to points in Korean history which indicated martial arts and also kicking, through Taekkyon, which is a Korean game based on skill in kicking or leg techniques.
"However, although there was a resemblance, it is in fact different." -- meaning Taekkyon is different from Taekwondo in that Taekkyon is softer and emphasizes pushing rather than striking. Early Taekwondo competition did have some focus on pushing kicks, but this was eventually phased out in favor of striking. However, Taekkyon does emphasize a relaxed manner in developing techniques, as compared to the Japanese explosive muscle contraction style.
"Should we consult [Taekwondo’s] historical origins, it could be persuasive to say that Japan adopted their martial arts form from the Chinese martial arts, and it flowed into Korea later. Japanese people scientifically developed them by making many modifications from the Chinese martial arts. It seems that there remained a problem. Japanese people put emphasis on muscle strength rather than on flexibility in the course of developing the form of exercise. Accordingly, you cannot avoid the body movement being stiff.” -- meaning even though we can say that Taekwondo partially flowed into Korea through Japan, there was a problem with Japanese karate because it is stiff and muscle oriented, which is not the Taekwondo way. Taekwondo therefore is a combination of the format of Japanese karate (standardized uniform, belt ranks, forms, and linear striking) but done in the korean way (relaxed explosiveness, rather than hard muscle tensing explosiveness, and emphasis on kicking).
In short, Koreans know that kicking is part of their culture, but how do you explain that to non-Koreans who want proof in the form of dates, documentation, and other "evidence"? So they did the best that they could, which is look at the historical records and books to explain their cultural affinity for kicking competitions.
Is it persuasive? Maybe not. But that is all they have to go on, which GM Lee admits was not much, especially since Taekkyon itself as an art is so poorly documented. It is so poorly documented that they could not even find chinese hanmoon characters for Taekkyon,which is why we have Taekwon, the closest thing to taekkyon. If there were chinese characters for taekkyon, then the art name would be Taekkyondo, not Taekwondo.
If that effort results in people thinking that all of this was "lies", then so be it. You can't please everyone.