This is a good synopsis of what the general public thinks happened thanks to pundits and talking heads but its pretty far from the truth. Also you have a slight mix up on the years, he was "slumping" 4 and 5 years ago. He's been in the league for 10 years so it wasn't "the next couple" after he came into the league.
What actually happened was that he was never slumping. He was doing exactly what his coaches told him to do. When Hunter was in DC he had Ovi blocking shots, loved Laich and Beagle, and essentially treated Laich as though he were the captain over Ovi. I usually say you can't argue with results, second round of the playoffs in '12, but in this case can't you?
Hunters coaching method was using the leagues best scorer to block shots. Every shot a team took that Ovi was back defending became a 10 million dollar bruise. That's not utilizing the best aspects of your roster. You might be able to credit him with recognizing he had something special in Holtby, but tons of coaches ride the hot hand in net and its frequently regarded as a weakness in their methodology. He didn't even fix problems he knew about, for example, admitting after he left that refs hate Semin and he never knew why. And no one is saying Ovi should be out for defensive zone faceoffs with 10 seconds left but to bench him for the final 2 to 5 minutes of the game? Including offensive zone starts? Hunter wasn't actually that good.
Everyone said Ovi was done and the league figured him out and he was never scoring 40+ again during his 30+ goal seasons of defensive play. Then Oates came in and taught Ovi how to play on his orthodox wing. Once again, he did exactly as the coach told him to and when he fully bought into the system, unlike some of the other players, he captured the Rocket in both of Oates seasons in DC.
Caps fans bought into the talking points about Oates the way everyone else bought into the talking points about Ovi. Its one of the best professional character assassinations I've ever witnessed. So undoubtedly a lot of people on here will say Oates was literally Hitler but he did a lot of good for Ovi and the team. Especially when you look at how Ovi handles criticism now and how much he enjoys playing again compared to how much criticism he was getting for doing as he was told when Hunter was there. He's back to his old self and a lot of credit is due to Oates, not because Ovi ever slumped, but because the media was destroying his low(ish) goal seasons.