Do you have any idea what the machine was measuring? My guess is that it was some sort of bioelectrical impedance analysis machine. Simply put, it measures electrical resistance from one side of your body to the other. Fat has a low water content, so it's a poor conductor. Muscle is high in water content, so it conducts very well.
The machine sends a pre-determined amount of electrical current from one electrode to the other and measures the resistance. The more resistance there is, the higher your bodyfat is. The problem is that the machines are very sensitive- you can't just walk in off of the street and get an accurate reading.
Ideally, you will not have exercised for 24 hours, have not eaten for 12 hours, are well-hydrated, and have an even distribution of bodyfat/muscle between the electrodes- if it's a hand-held device, it's reasuring resistance from hand to hand, if it's a scale-type device, it's measuring from foot to foot. Now, think of how women differ as far as upper and lower body fat...

So, if you had been exercising, eating, a little dehydrated, or a little dis-proportionate in your fat distribution, then the machine is going to overestimate you. The best way to get bodyfat analyzed is with a DEXA machine or Bod Pod. Next best would be skinfold measurements, but you have to be VERY picky about who takes the measurements. I'd recommend calling up your local University and looking to see if they have an Exercise Science department. There, you'll find people that do skinfold measurements on a regular basis, and who know the exact sites to measure (critical for accuracy).