Given the obvious seriousness of the situation, we can take it in a good faith that Scotty wasn't screwing around but serious and correct when he stated "No question, Their power is simple impulse."
Serious we can bet on. Correct doesn't follow.
It's an interesting strawman argument. Still, Scotty at no point claims impulse is STL. On the story points, Scotty and the crew are correct:
1. Simple Impulse is slower and allows the Enterprise to chase or run away in "The Balance of Terror" at "maximum warp".
2. At no point does any crew or Scotty indicate that a mistake had been made in their technical analysis of the BOP.
3. In "The Deadly Years", the BOP continues to be slower than the Enterprise when she goes to Warp 8.
The only speculation is on our part on how fast "simple impulse" is in TOS.