It hard to say without knowing what "treatment" was applied, however it doesn't sound like it was anything permanent or robust if the paint has all of those defects. Some stealerships apply sealant and call it a "treatment." Sealant is basically a more robust wax that can last up to a year.
The process of "buffing" to paint correct is the process of removing the clear coat around the defects, to level the clear coat at the lower level of the defects, so they are no longer visible. Paint correcting will remove any treatment that remains on the paint after thoroughly washing the car, because you are literally shaving the clear coat, and anything applied on top of it, down.
I would recommend a very, very thorough wash, I know detailers debate this a lot but I mix dawn dish soap in with the car wash to strip everything I can off the paint. Then I would suggest using a clay bar and IronX to get the paint as clean as it possibly can be. (Be careful with iron removers, and clay bars, they can damage the paint if you don't know what you are doing.)
Definitely do a test spot, I used Meguiars D300 with a microfiber pad on a DA polisher (Microfiber is considered aggressive, but you can control that based on how long you polish and how much pressure you apply). I did not correct the paint to 100% because I did not want to remove that much clear coat, I probably did a 60-70% paint correction and it looks amazing unless you really stick your nose up against the paint. I follow that up with Menzerna SF3500 polish to bring back the shine after the paint correction. Paint still looks fantastic three years later with a coat of sealant once a year and wax every 3-6 months.
