So, all of these cases are public records. The federal level stuff is all available quite openly on the web. The state stuff is a mixed nightmare of fifty different systems at the appellate level (which is the stuff that is usually cited). At trial court level you have (literally) 3000 different systems, most of which are not accessible for LLMs.

But yes, 100% LLMs should be able to check themselves. Another poster below brought up the other issue is that you can check the citation and it's 100% correct, but that it doesn't legally apply to what you are writing, and/or it doesn't mean what the LLM thinks it means in the limited context it has taken it from.