It can be possible. Now, here's another made-up method:
1) Start a new game file, and save the Oxide Station time relic for last.
2) Beat N.Oxide's ghost in the course before you obtain the relic.
3) Beat the course, and challenge Oxide.
4) You, Oxide, and his ghost are on the track. You'll notice that they make the same movements each time, only one drops projectiles, and can get hit.
5) After beating the course, three unusual captions will appear on the screen, "Platinum Relic Obtained", "N.Oxide unlocked!" and "CTR token obtained!" Very weird.
6) Now check your character menu for a pleasant surprise.
If you see me posting, it's because I've been asked to. Which I guess would mean I'm taking requests.