[Boromir88]

Sam, who doesn't think best with his head, and knows absoloutely nothing about medical stuff could easily believe Frodo to be dead.~Azaelia

And this makes sense with Tolkien's writing style. First, he sets up a difference between his characters and himself. (As in Letter 153 when Tolkien singles out Treebeard and says he's a character in his story not him). The knowledge, independency, and opinions of his characters are incorporated into the story. They may or may not always be right and they could certainly be fully of baloney. This makes sense with someone like Sam who sees Frodo there limp and not moving. Having no experience of this prior he would not know that Frodo was merely poisoned, where the Orc patrols who probably experienced this with Shelob several times, or were aware about it noticed that Frodo was indeed not dead.

Also, to explain Eomer who as mentioned was just grieving over the death of Theoden, now he sees his sister lying there not moving. Someone you forgot to mention Mith is Faramir who was perceived dead, but Denethor was not in the right state of mind during this.

The other thing about Tolkien's style is that he is much more of an "in the moment" sort of writer. Not really giving a look ahead to his readers, it's a what is known up to that point. Tolkien being the omniscient narrator is not bound to tell us all that he knows. In instance is with the Balrog. At first with Durin's Bane who is referenced as "It," (even by our omniscient narrator):

It came to the edge of the fire and the light faded as if a cloud had bent over it. Then with a rush it leaped across the fissure. The flames roared up to greet it, and wreathed about it; and a black smoke swirled in the air. Its streaming mane kindled, and blazed behind it. In its right hand was a blade like a stabbing tongue of fire; in its left it held a whip of many thongs.~The Bridge of Khazad-dum

Also throughout this chapter Gandalf refers to the balrog as "It." Then later a gender is given to the Balrog:

"Name him not!" said Gandalf, and for a moment it seemed that a cloud of pain passed over his face, and he sat silent, looking old as death. "Long time I fell," he said at last, slowly, as if thinking back with difficulty. "Long I fell, and he fell with me. His fire was about me. I was burned. Then we plunged into the deep water and all was dark. Cold it was as the tide of death: almost it froze my heart."~The White Rider

So, the point is Tolkien acted much more like a recorder telling us the story. What is known by his characters at that point in time and he does not reveal to us all knowledge that may come to us later. It's what is going on at this time, and what is known at this time.