thinking as myself... I'd be annoyed if I was a Trojan and I'd spent 10 years resisting a siege, and then it had all gone to nothing because the city fathers decided to fall for a stunt like that.
But thinking as someone who lived thousands of years ago and had never read Homer and never knew how tricky Greeks were, I'd probably have fallen for it myself. It is difficult to put ourselves in the minds of people who lived long ago and knew almost none of the things we know now about history.