Are claims that adult spines even in their late 30s can grow more than 2 inches? Besides improved posture are there rare conditions that can cause it?

In fantasy land. If you had scoliosis and waited until you were in your mid-30's to have a surgical correction, then that might account for it. Another scenario might be if you decided to start wearing high heel shoes and slacks so no one else would notice that you were but they would notice your sudden height gain. Otherwise, no can do!