The Fae can be killed,  Aurora was killed by steel box knives, Maeve, by a bullet, Lily, by a bullet.
Jim is going by the Tolkien rule for elves, they are basically immortal but they can be killed by violence.

“Right, then!” Bob said. “The only way to kill an immortal is at certain specific places.”
 “And you know one? Where?”
 “Hah, already you’re making a human assumption. There are more than three dimensions, Harry. Not all places are in space. Some of them are places in time. They’re called conjunctions.”

“Maeve’s an immortal, Harry. One of the least of the immortals, maybe, but immortal all the same. Chop her up if you want to. Burn her. Scatter her ashes to the winds. But it won’t kill her. She’ll be back. Maybe in months, maybe years, but you can’t just kill her. She’s the Winter Lady.”

Changelings who choose get eternal youth but they are not immortal. They get killed on a regular basis and do not reform like the queens do.

They can die under specific circumstances. Really immortal here means just more difficult to kill.