We will have to agree to disagree. I've seen Hwang Kee use them like so.
We could agree to disagree if this were an opinion type issue, but it is not. It is a factual one. The fact of the matter is "traditionally", which hopefully you mean from the beginning, Tang Soo Do and Soo Bahk Do utilized short stances. When did you see GM Hwang use long wide stances?
And here's where every dispute about the martial arts begins and ends: The lack of source material.
Maybe you have a lack of source material but others are not so limited. For example, if you look at GM HWANG Kee's 1958 book Tang Soo Do Kyobon, it shows the stances are short and narrow, not long or wide. This book was written when the name Tang Soo Do was used by GM Hwang and two years before the Soo Bahk Do name was used.
How did one school or even one country impact another is largely conjecture. In fact, there is an argument that the martial arts began with the Greeks and came to Asia by the way of Alexander the Great.
I don't know about the Greeks or Alexander the Great, but I think that there is documentation on how Karate traveled from Okinawa to Japan to Korea.