It's not impossible at all. I have a very small frame. According to my manual for my skin fold calipers, at my height, an elbow width of less than 67mm indicates a small frame. My elbow width is below 55mm.
MY hubby isn't home to measure my skinfolds right now, but please, put your mind at ease, I do indeed have plenty of bodyfat. Last time I measured it was 27.8%. That was a while back, and I've lost some weight since then.