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!... A Sonic Origins (SO) Sound Mod in the Music category, submitted by PimpUigi
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