I know that this post is two years old and that muffster already passed(hopefully by now) that roadblock with their Togetic but according to Bulbapedia and my recent playthrough Platinum, the best answer is wrong. In Bulbapedia it states that, "In Pokémon Diamond, Pearl, and Platinum only, obedience is determined by the number of Badges, not which specific Badges the player has."
From the chart these are the Badges by obedience level: (Note! For D/P/PL only)
Up to Lv. 10 - No Badges
Up to Lv. 30 - 2 Badges
Up to Lv. 50 - 4 Badges
Up to Lv. 70 - 6 Badges
All Pokémon: 8 Badges
In my current playthrough of Platinum, I have only three badges and my traded Gengar won't obey since its Lv. 32. It won't start obeying until I receive my fourth badge. The same goes with muffster's Togetic.