Primeiro note que Faramir não recuperou a buzina do barco de Boromir (ênfase minha):
'A broken sword was on his knee. I saw many wounds on him. It was Boromir, my brother, dead. I knew his gear, his sword, his beloved face. One thing only I missed: his horn. One thing only I knew not: a fair belt, as it were of linked golden leaves, about his waist.
[...]
The horn of Boromir at least returned in truth, and not in seeming. The horn came, but it was cloven in two, as it were by axe or sword. The shards came severally to shore: one was found among the reeds where watchers of Gondor lay, northwards below the infalls of the Entwash; the other was found spinning on the flood by one who had an errand in the water.
The Two Towers Book IV Chapter 5: "The Window on the West"
Dito isto, a questão de por que Faramir não tentou recuperar o corpo de seu irmão é sensata, então continuarei com ele.
A única explicação dada no livro 1 é que Faramir "não ousou" tocar no barco (ênfase e link meu):
Faramir acreditava claramente que o barco era mágico e peculiar, e os homens de Gondor mostraram-se supersticiosos em algum grau (veja os comentários de Boromir sobre Lothlórien na Fellowship , por exemplo); normalmente é considerado bom senso deixar coisas mágicas e peculiares sozinhas.Then I saw, or it seemed that I saw, a boat floating on the water, glimmering grey, a small boat of a strange fashion with a high prow. and there was none to row or steer it.
'An awe fell on me, for a pale light was round it. But I rose and went to the bank, and began to walk out into the stream, for I was drawn towards it. Then the boat turned towards me, and stayed its pace, and floated slowly by within my hand's reach, yet I durst not handle it.
The Two Towers Book IV Chapter 5: "The Window on the West"
Outra explicação possível é que ele foi compelido por alguma força externa a deixar o barco sozinho; mas não temos informações suficientes para especular sobre quem exatamente (embora fosse quase certamente Ilúvatar ou um dos Valar) teria feito o atrativo, ou porque eles teriam se incomodado.
Infelizmente não há clareza a ser encontrada nos rascunhos de Tolkien, apesar de ser fascinante ler a evolução da história