I think the difference is that it's more obvious that aliens in NJ are a joke. Armed men kidnapping children from schools in Mexico is an entirely realistic scenario that any reasonable person should expect to cause a panic.
It's almost like that but times have changed. In 1938 it was mainly a broadcast of a message which then wasn't easy to broadcast again by the people. Nowadays you broadcast something and in a couple of minutes it can reach the whole country just because of re-tweets and mobile messages. The end result can be a good number of times worse because of this.
Or maybe we should think twice about saying things like "your kids are being killed at school". I am open to suggestions but I have never heard about a book causing mayhem in a couple of minutes.
The reason why is that people don't expect to trust books. Open a random book at the bookstore, and it's probably a story that the author made up. Twitter is the same way, but people don't realize this yet.
I don't see why authors should be held responsible for their readers' stupidity, though.