I experienced something similar with my cat, Cleo, several years ago. She used to be quite overweight (actually obese), had dandruff on her back and was sensitive in the area above her tail. Once I got her onto a canned only diet, and she lost about 5 pounds, she was able to groom the area again, and the dandruff and irritation went away.
Like you, I couldn't see anything in that area other than dandruff, but I think the spot was tender because she couldn't reach it to groom.
I'm sure there might be other reasons for her behavior, but that is the experience I have had with my own cat.