"In the news" means that a subject is currently found across all news media - on TV or radio news broadcasts, or in newspapers etc.
eg "The story has been in the news this week".
"On the news" would be used to refer to a specific news broadcast or source.
eg "I saw it on the news last night".
Your example using "at the news" could refer to hearing "news" from any source, not necessarily "news media". It could equally apply if an individual told you something important to you personally but not "newsworthy" to anyone else.
They reeled in horror at the news that their aunt had died.
It means that they reacted upon hearing whatever they have been told. You could not interchangeably use "at" with any of the other examples using "in/on".