Yes and can they sue for this too? Not sure how it works but this does sound it is like creating unfair stress for people to have to now defend themselves because they retweeted something or expressed an opinion on twitter.
I have the impression that being charged with a crime has permanent consequences even when it is rapidly dropped.
There may be rules about how people and organizations aren't supposed to hold it against you, but if records are retrievable then it won't go away.
Someone with more legal knowledge might chime in, but I feel like I've seen questionaires asking something like "have you ever been arrested, charged, or convicted of a crime..."
It's like in court when the judge tells the jury to disregard something, can they ever really do that 100%?