No, this isn’t correct.
The number of Titan Parts is tied to both Loot Tier and hitting the Harpoon Target Levels.
Tracking for that has started over here: Titan Parts Loot Tier Drop Tracking – show me your drops
Additionally, it’s likely that the rarity of the parts dropped is related to Loot Tier, in the same way that higher star Titans have better chances of dropping rarer Ascension Mats in those slots.
So higher star Titans at the least have more rolls for Titan Parts, and likely also will give more of the rare ones on average over time.
You’d also obviously be significantly reducing all other Titan loot just to chase Titan Parts, which are mostly useful for killing bigger Titans…if you’re already successfully killing bigger Titans, that seems a bit counterproductive to me, unless you were just trying to stock up in anticipation of 13* and 14* Titans.