The flight from the Nazgul: did the High Elves care?

Originally Posted by Raynor

The elves weren't aware of the importance of Frodo's travel. By taking them along, they performed a simple act of kindness towards persons stalked by the Black Riders.

They knew that Frodo's errand was of great importance, & they were also concerned that Gandalf was not with them. When the Nazgul come all the way from Mordor to the Shire, it must have struck them that they were after something of great importance from the Hobbits. The simple truth is they felt this tale was none of their business, & did the minimum they felt was needed to comfort the Hobbits.