Why did Priam insist on staying in the Greek camp before departing with Hector's body in the Iliad?

As Priam explains to Achilles, who has finally agreed to give him the corpse of his son Hector, he is very tired. He has not slept for days, because he has been weeping and mourning for his son. Now that he has eaten a big meal and knows he will get his son's body back, he is overcome with exhaustion. Therefore, he says he will stay and sleep in the Greek camp.
The risky action shows that Priam feels safe with Achilles, despite the two being mortal enemies. They have connected, albeit momentarily, as Priam is able to persuade Achilles to imagine how his own father might feel were he, Achilles, is killed and his father not able to bury his corpse. Achilles understands that and, urged as he is by the gods, relinquishes Hector.
However, as Hermes reminds Priam when he wakes him up at night, the idea of safety is an illusion. Hermes tells Priam to leave the Greek camp immediately, before a great deal of trouble comes his way.