Should possibly inflammatory Tweets be protected as free speech?

Spurred by two British cases reported on NPR. In one, a guy has been prosecuted for threatening to blow up an airport that had delays in a Tweet to his girlfriend. In a second, a government official sarcastically tweeted that a militant Muslim who protested the West’s criticism of stoning should be stoned by someone. I’m not sure if he is being prosecuted or was just made to publicly apologize. Were both credible threats or annoyed remarks? Should they be prosecuted? Your thoughts?