There are about 33 million Saudis. I doubt most of them had anything to do with this, and I think it's important to maintain a mental distinction between the government of a country and its people.
e.g. "Did the Americans know about Pearl Harbour?" "Why did the Soviets develop the atom bomb"? "Why do the British maintain a nuclear deterrent?" "How will the Australians react to the detention of one of their nationals by the Chinese?"
The 32m+ citizens are called 'Saudi Arabians'... calling them 'Saudis' is, erm, informal at best, lazy at worst?
Technically, they're overwhelmingly correct, and your definition is in fact the uncommon one. For example, see the primary definition for both adjective and noun usages in the Oxford Dictionary of British & World English (not even US English).
I agree that people generally understand that in this case the headline refers to the Saudi government - but OTOH, this kind of "generalisational" language can perhaps be a form of propaganda, or at least subconsciously change some readers' perception with constant exposure.
That being said, it's still pretty normal to speak like this. Americans, Russians, Chinese.
The Saudis = the Saudi Family
Saudi Arabians = all Saudi citizens