It's important to keep in mind how the particular product you are using actually works and the effect it has on your clear coat. Polishes and compounds remove stains etched into your clear coat by actually removing a very tiny layer of the clear coat. The more abrasive the product, the more clear coat it removes. That is why you want to start out with the least abrasive product first and then work your way up. So I think something like vinegar or a paint cleanser is great to start with and hopefully that would remove the stain. But if that doesn't work, I would then next try a polish, and then only if these did not work would I use a compound.
It also speaks to the value of regularly protecting your paint with sealants, waxes, ceramic coatings, etc so that you can reduce the need to polish and compound as much as possible in the future.
Please do let us know what product actually worked to remove the stain. I am really curious in case I run into a similar situation.