Some historians, and particularly those tied to the WTF and associated bodies, have a tendency to use Taekkyeon and Subak as the foundation of this theory.
To support this, they then revise the history of the formation of Taekkyeon back to the Three Kingdoms period (with some solid evidence, but remains contested admittedly). Subak apparently has more evidence linking it back earlier than Taekkyeon, which is why the two are lumped together as a sort of two-pronged approach at evaluating the ancestry of modern TKD.
There are reasons for this, including marketing, validity in the eyes of classical martial authorities, and probably most influential is the fact that Korea after many wars had struggled with a sense of cultural heritage or identity - using TKD of the 20th century to act as a sort of "inheritor" of the older Korean martial arts, despite the aforementioned classical arts still being practised today.
Remember, the South Korean army (still does?) or at least did enforce modern TKD as a basis for their non-weapons martial curriculum. This was a calculated endeavour to entice a sense of national pride, regardless of how ineffectual it might be in modern warfare CQC.