The trans-national nature of the Houthi rebellion undeniable. And based on historical grievance as is mentioned in this Strategy Page article:
"Yemen: Fantasies Crumble And Turn To Dust"
"The Saudis also know that this border area has been the scene of Sunni Shia conflict for a long time and so far the Shia have resisted conquest by being so tough that the cost (in lives and cash) was never worth the Sunni effort to crush Shia power down here. The western border area has been occupied by Shia tribes for centuries. The current border was only established, by force, in 1934 when the Saud family created Saudi Arabia. This was done with a largely Sunni tribal coalition organized and led by the Sauds. Some of those tribes were Shia and are just across the border from similar Shia tribes in Yemen. The Sauds have treated their Shia tribes well and the Saudi Shia obviously live better than their Yemeni cousins. That is largely why there has been no unrest from the Saudi Shia tribes. But the Yemeni Shia have always believed that the way the Sauds drew the border 80 years ago unfairly took land belonging to the Yemeni Shia and now these long simmering disputes have added to the animosity between Saudis and many Yemenis."
Thanks to StratFor we have this map of the Arabian Peninsula showing those areas Shia and Sunni. Judge for yourself that serious nature of any threat as posed to the Saudi by a restive and cantankerous Shia population.
NOT ONLY THE EUROPEAN COLONIAL POWERS HAVING DRAWN BORDERS ON A MAP REGARDLESS OF TRIBAL, ETHNIC, OR NATIONAL CONSIDERATIONS. THE SAUDI ALSO HAVE DONE SO AND IN A MANNER IRRESPECTIVE OF RELIGIOUS AFFILIATIONS AND THIS NOT FORGOTTEN!!
Historical grievance the amelioration of which is next to impossible even negotiated and amicable settlement now out of the question?