The loyalty of the vassal government to you is irrelevant because the rebels are rebelling against that government. It's an issue of the AI's inability to take measures to prevent internal revolts. You see your vassals collapse a bit more often than other empires because they have lower AI bonus (particularly the stability part is relevant), the circumstances of vassalage cause unhappiness for several factions, and possibly because the AI is in an economic mess due to taxes. Basically, imagine you are the USA, your subject is the Karzai or Ghani government in Afghanistan, and the rebels are the Taliban.
Ideally the AI would be less inept at dealing with revolt situations, but if that can't be done, we could do with some way to track and possibly intervene in such situations in subject empires. While it can sometimes be fun to use claims granted by rebellion, shout "doctrine of lapse" and start assuming direct control in the style of the British East India Company, sometimes you just want your vassals not to be basket cases.
