Who explains the death of Polonius to the King? Does she give an accurate account? why or why not?

Gertrude explains the death of Polonius to Claudius, 

Behind the arras hearing something stir,
Whips out his rapier, cries, “A rat, a rat!”
And in this brainish apprehension kills
The unseen good old man. Act 4 sc 1

That is pretty much the way it happened. I don't think Gertrude has any reason to alter the truth at this point.