This is incorrect. You just need a PC and a ROM of S3&K. That's it. You don't need to buy any S3&K unless you rip the ROM yourself.
Also, as a reminder:
If you have Sonic Origins and want to fix the soundtrack, you can do so here:
The best Sonic 3 OST of all time!... Download the The Definitive Sonic 3 OST Sound Mod for Sonic Origins. Customize your gameplay with this fan-made SO Sound Mod by PimpUigi in the Music category,
gamebanana.com
It's very easy, just copy the files provided in the ZIP into the sounds folder which is located here:
Steam\steamapps\common\SonicOrigins\image\x64\raw\sound