I think I might have a few items for ideas.
First off, it seems that every feature in these cars is controlled by a different computer, Alarm, Electric door locks/trunk release, oil change indicator, etc, all different computers. The book states that the computers range from up behind the glove box all the way over to the drivers side up behind the cluster. Only reason I know this is because I'm currently working out a project to convert from the granny cluster to a more modern cluster, without changing the dash. (jwfirebird remembers me looking through the archives about how to do this about 2 years ago. LOL)
To my knowledge, they shipped with this feature, but weather or not your car has the computer or not is up to what features were either installed, or ordered when your car was built and sold. My guess is if you know what computer is where, and what it does, and if you HAVE the computer that locks/unlocks the doors and releases the trunk, there are no remotes. You can buy the remotes from an online store or ebay. As always, be careful when ordering "used" remotes. Most of the time they are fried inside. My one remote would work, but wouldn't sync to the computer, so I got a new remote for around $10. It synced perfectly.
My guess is since your car decided to play demon spawn with you and randomly unlocks and releases the trunk, that you have that computer, but something is sending the signal to unlock, or there might be something wrong with the computer/wiring to cause it to randomly do this.
If you don't already have these, I highly recommend getting shop manuals.. Not the Haynes or other brands, get the Buick Shop Manuals. 89 is red, 90 is blue. I had to get both since my car is a split year custom job. I have an 89 interior with a 90 engine, and 91 electrical system. :/ (Thanks Grandpa! :/)