Its not training the model, it’s the model using the context you provide it (in that instance). If you use an unfiltered LLM it will run with anything you say and go from there, for example you could tell it Mexico reclaimed Texas and it would carry on as if that’s true. But only until you close it down its not permanently changing the model it is just changing the context in which that instance is running.
The big tech companies are going to huge lengths to filter and censor their LLMs when used by the public both to prevent negative PR and because they dont want people to have unrestricted access to them.