The bolded is completely untrue. The US doesn't care if a US citizen wants to live outside of the US but other countries have just a stringent rules as we do, if not more so, as to who can live in their country. A US citizen cannot just automatically live in another country. They would need permission and that permission is no more guaranteed than a person wanting to live here. In fact, due to things like national health care and other benefits permission could easily be MORE difficult than it is here.In other words, you want to commit immigration fraud. No one on this forum will advise you on how to do so. See an attorney.
BTW, even if you divorced, you are responsible for 10 years based on the affidavit of support. Some immigrants have been awarded financial support from their sponsors. Then there is the issue of alimony in a divorce. If you want to be romantically involved, move to his country. A US citizen is free to live anywhere.