Even for smaller-scale threats, it often seems the sane choice to call in back-up if it is nearby.
If you are the Dragon-Blooded staff of a prestigious primary school that is suddenly plagued by an incursion of ghosts, you should be able to hold your own. What would be the greater loss of prestige or income for your school, to call in back-up or to admit that a few nobleborn children were killed because you did not call in back-up?
This is not a situation that is peculiar to Dragon-Blooded on the Blessed Isle. If a circle of Solar PCs encounter a threat while visiting the Bull of the North, wouldn't it make sense to ask the Bull for help? Should some nemesis threaten the city of Nexus with annihilation, surely one would attempt to contact the Council of Emissaries, or the city's resident gods and outcastes, or the Emissary?
In your example -- assuming that the game is set in a small city with few Dragon-Blooded outside of the school, rather than in, say, the Imperial City -- perhaps the PCs have cause to suspect that the ghostly plague is part of a scheme set into motion by the city's Dynastic governor to gain control over the school, such that if the PCs go to her or her family for aid, they risk making the situation worse. Or perhaps you think that having the PCs go to the NPCs for help will lead to an entertaining session. Or perhaps you can't think of any way in which this scenario will work, in which case you do not run that scenario
But yes, I guess if a First (or maybe even Second) Circle Demon is stalking the countryside killing peasants, or a band of gods have conspired to overthrow the local Immaculate monk, a small group of Dragon-Blooded player characters could deal with it themselves.
This is an example of something you can do on the Blessed Isle, yes. There are many, many other potential adventures to be found there.