You're correct! (That was the main error, anyway.)
Yes, Peppy and Slippy never come down to the planet, and the other mistake is that Krystal is never in that room. On the cover, they're all in a room in Krazoa Palace where you get the last Krazoa Spirit from General Scales. Krystal wasn't freed until after Fox got all the spirits, so she couldn't be there either. (Not to mention Tricky, who can't usually warp, and you must warp to get into the aforementioned room.)
And Watoad, I did go look up the cover, and thereby made sure I was right. It was kinda small though, so I couldn't see much else besides the Ocarina.