Odd, the one time I made birch beer it carbonated, not heavily, but then I don't want much carbonation with birch beer. I'm certain it was "Old Fashioned Homebrew" extract that I used.
If you have some of it still around, why not pour a bottle into an open container and let is sit at 80F for a few days? Check to see if the gravity changes.
Remember one unassailable statistic, as explained by the late, great George Carlin: "Just think of how stupid the average person is, and then realize half of them are even stupider!"
"I would like to die on Mars, just not on impact." Elon Musk