My best guess is that they were trying to reconcile Nimbus III in ST V -- formed by a treaty between the UFP, Klingons, and Romulans -- having been around for 20 years when there'd been no contact with the Romulans prior to "Balance of Terror" in late 2266. So they figured they had to push ST V back to 2287, and that meant pushing up II-IV as much as they could.
But if that's true, I don't see why they bothered. The 20-year figure could've been just a rough estimate, as much as Khan's 15-year figure.