Interesting. I happen to know what my approximate lean body mass is, so I can estimate my body fat based on my fluctuating weight pretty accurately.
Right now, my BF is about 30% and that calculator was spot on.
Just out of curiosity, I keyed in my measurements from when I had a 19% body fat (measured in multiple ways) and it said it would have been 23%.
I think it's probably less accurate (or more sensitive to body shape differences) when your body fat is lower. When I was 19%, my upper body was somewhat emaciated, but my lower body still held visible fat. That calculator can't tell that with no chest, back or arm measurements (my neck measurement has never changed). Someone who was more apple shapped than me might see a lower than accurate number (small hips). Yep, just keyed in DH's numbers from when he was at 6% BF (body builder) and it said he was 3%.
In general, it's probably a fairly decent gauge if you aren't already quite lean.