Just in case anyone else here runs into this problem:
If you've gotten TS2:UC free from Origin & out of nowhere, you go to play your game & get "The Sims 2 is not installed on this system, or some required files have been deleted. This expansion pack requires The Sims 2 in order to run. Please install The Sims 2 before attempting to run this application.", you should apparently go into Origin > My Games & right-click TS2 & choose "Repair Game." Evidently this makes it all better. I wish I'd checked before I'd uninstalled & reinstalled it the first time I got that error. I can't vouch for the efficacy of the repair, because it's going as I type, but I hope this helps anyone who gets this scary error.