I suppose you could say Herodotus is recording something the Spartan's wrote about themselves which is likely to be exaggerated.
I don't know who's orders the Spartans refer to. The history I've read on this says the Spartans insisted on standing their ground in the councils that were held with the soldiers of the other Greek city-states. So they followed their own orders and are dead.
Exaggerating the numbers involved in a battle? I'm sure that never happens.
The Spartan Epitaph was written from the point of view of the soldiers who died, saying they took the orders of the Spartan government (primarily the Ephers) who had sent them to Thermopylae. Like Nelson, they could have said, "Thank God, I have done my duty." But that is less evocative.