According to online BMI calculators which only use your height and weight to deduce body fat, it calculates your numbers at 18.4% which is technically under weight. 18.5-24.9 is optimal weight without any other factors to take into consideration.
A scale shouldn't really do any more than that, except it may use some kind of inductive measurement through your skin, but even that is nothing as compared to calipers.
That's my size also. If your belly protrudes, it is probably more to do with bloating from gas or constipation. I don't know how digestion is working for you or what you're eating, but that's how it is for me. I can pinch less than an inch of fat over my abdomen, so I have just enough fat for me to feel good. But I have slow digestion, and trapped gas or stool ruins my shape. You may just need to add more fiber, such as an apple and more water a day, or perhaps you just need Metamucil. This is assuming you have ab muscles, but when you're bloated it can be hard to find them.
That is actually extremely helpful considering I have stomach issues after anything I eat and I go days without a bowel movement. I will look into adding more fiber to my diet. Thank you for your help!