I'm going to make an argument for the potential use of "got off" here. If someone is in trouble for something, he/she stands the chance of being subjected to several different punishments or to none. For my example, I will use someone who has been stopped by the police while driving and found to have been drinking alcohol.
Mr Smith was arrested on Saturday night for drink-driving. He was found to be twice over the legal alcohol limit. He was kept in police cells overnight and appeared in court on Sunday morning. The judge had several choices: imprison him, ban him from driving, fine him or release him with only a warning. Mr Smith was very lucky. The judge was in a good mood, considered the fact that it was Mr Smith's first offence and decided on the latter punishment. So Mr Smith got off with a warning.
Basically, he "got off" because he was not jailed, banned or fined. He was let go after a warning not to do it again.
