There are a few studies that have compared the BIA scales with DXA and other means. The TL/DR is that they are fairly accurate for the population in the middle of the bell curve. For people with very high or very low body fat or very high muscle mass, they are less accurate. They overstate bf in lean cohorts and understate in high bf cohorts. If you have a scale with an "athlete" mode, you should be using that, as it will skew the results towards a more lean/muscular person.
I find they are useful for looking at the delta over time and for tracking hydration. I try to take my readings at the same time every day and hopefully around 50% water. If I'm over hydrated my bf will show low by 2-3%. If only it were that easy. Conversely if I'm a little dehydrated my bf will read high. I'll disregard those results and stick to using the ones from 49-51% BW. Knowing how they derive the bf% is crucial. The electrical impedance that is measured is applied to formulas that take into account your age, height, and weight. Since it is normal for your weight to fluctuate by +/-5lbs, this will effect your bf readings as well, although to a lesser extent than the body water. So again, good tool for tracking progress over time, bad tool for trying to get an accurate measurement on a given day.
By the way, I've found some Groupons for really cheap DXA scans. I try to get one once or twice a year.