Precision != Accuracy
You can be very precise in your measurement and your measurement can still be very wrong.
For example, if I had an extremely precise height measuring system (a super ruler) and I measured my height to be 82.23535cm, and later found out that I had mis-calibrated the system and my height was actually 182.23535cm . . . well, my previous measurement was still very precise. However, it was not accurate. That's the difference.
So, the conclusion is that no matter how good your instruments and observational techniques, if your calibration is wrong, or if you interpret the data wrong, you get very precise inaccurate numbers.