Eu não acho que eles podem ser prejudicados pelo fogo, eles simplesmente não apreciam ser empurrados em seus rostos.
Como a citação em si diz, eles não temem o fogo - eles temem aqueles que o manipulam. Qualquer um que esteja empunhando um fogo na cara deles obviamente tem (a) conhecimento sobre Nazgul, e (b) tem estatura suficiente para não se tornar um naufrágio em face do medo gerado por eles, então o ato de empunhar o fogo em um Nazgull em um sinal de que o inimigo deve ser levado a sério.
Em Carta 210 Tolkien toca nisso:
Their peril is almost entirely due to the unreasoning fear which they inspire (like ghosts). They have no great physical power against the fearless.
Além disso, o fogo não foi a principal razão pela qual os Nazgull fugiram de Weathertop. Tolkien escreveu sobre isso em um ensaio (The Hunt for the Ring) reproduzido em O Senhor dos Anéis: Companheiro do Leitor .
[The Witch-king] had been shaken by the fire of Gandalf, and began to perceive that the mission on which Sauron had sent him was one of great peril to himself both by the way, and on his return to his Master (if unsuccessful); and he had been doing ill, so far achieving nothing save rousing the power of the Wise and directing them to the Ring. But above all the timid and terrified Bearer had resisted him, had dared to strike at him with an enchanted sword made by his enemies long ago for his destruction. Narrowly it had missed him. How he had come by it — save in the Barrows of Cardolan. Then he was in some way mightier than the B[arrow]-wight; and he called on Elbereth, a name of terror to the Nazgûl. He was then in league with the High Elves of the Havens.
Escaping a wound that would have been as deadly to him as the Mordor-knife to Frodo (as was proved at the end), he withdrew and hid for a while, out of doubt and fear both of Aragorn and especially of Frodo. But fear of Sauron, and the forces of Sauron's will was the stronger.
Se não fosse pela combinação de resistência, a espada Barrow de Frodo e o grito instintivo de Elbereth, os Nazgull teriam persistido em seu ataque. O fogo não teria sido suficiente para impedi-los.