This is not true, both did play together in the season Dortmund reached the final. Don't you remember Reus playing in the final against Bayern when Gotze was injured?
Having said that, I agree with the general gist of your post. Klopp is a top manager, one with a unique playing style, his work at Dortmund is amazing no matter what way you put it, he built the great Dortmund team that won the league twice in a row and reached the finals of the CL beating teams like Mourinho's Real Madrid en route to the final. The only reason he doesn't have a CL to his name is because they played Heynckes Bayern which was one of the best teams in European football in the past 10 years. How anyone can argue that Klopps work at Dortmund is anything less than phenomenal is beyond me. He's a top top coach, if he wasn't he wouldn't be consistenly outsmarting world class coaches that have much superior squads to him ala what he did with Mourinho's Real, Heynckes Bayern (in the league) and Pep Guardiola's Bayern (in the two supercups).
All due respect to Conte, whom I also rate as a very good coach, but Klopp has definitely proven more imo. If for anything, for his prowess in the CL which Conte hasn't come close to matching.