If you weighed the same, but your waist and other measurements decreased by a significant amount (I'd call 1 inch significant as long as you are measuring under similar circumstances), then you likely shed some fat and gained some muscle.
Unless your trainer has done bazillions of caliper measurements, I wouldn't put too much faith in the bodyfat calculation.
James 1:16-17 ESV
Do not be deceived, my beloved brothers. Every good gift and every perfect gift is from above, coming down from the Father of lights
With God's help...Mens sana in corpore sano