 Why was Peter Karson initially relieved when he first heard the news of the invasion?
The order was made public early this morning by R. Stein, Secretary of the Council, who said in part: "The reason for this ... order must be apparent to all civilized peoples. "Since the Invaders first appeared in Wood River, Oregon, 24 hours ago, they have not once acknowledged our attempts to communicate, or in any way taken notice of our existence as reasoning beings. They have examined us, dissected us, driven us mad, killed us with no discernable provocation; and this is more intolerable than any normal invasion. Peter sank back in his chair, the full shock of it striking him for the first time. " Peter took it in fifteen seconds, running, and stumbled to a halt in front of the door marked "Radiation."
 It confirmed that what he saw was real, and he wasn't losing his mind.
 He was glad to know he wasn't the only person who had seen something.  He was glad to hear it reported, rather than ignored.  It confirmed that what he saw was real, and he wasn't losing his mind.  He feared he was going mad and was relieved to hear something from the real world.