I was thinking along the lines of some kind of ELECTRICAL INTERFERENCE. There are many stories of Electrical Interference Interfering with Instruments on such vehicles as Airplanes and Ships, and Motor Cars, etc. And one area of the World in particular is known to be a source of strange events possibly caused by some kind of Electrical Interference, 'The Bermuda Triangle'. Also such Electrical Interference is said to have occurred many times when near to UFO sightings.Excellent point, if a geiger counter is just registering voltage pulses across a sensor using a few hundred volts, then what if there was ambient electro magnetic energy at sufficient strength?
It's very unlikely that any readings on a geiger counter would be because of electrical interference. These instruments measure ionisation of a gas in a tube. Only something very energetic like radioactive particles or gamma rays are likely to cause that ionisation. The instruments are designed to measure radiation. So there are only two reasons why it would react:
1. There is ionising radiation present
2. The instrument is faulty, but this would not be selective around the tent only.
Also, there is very real and definite radiation on the clothes samples, so if a Geiger counter also responded around the camp site why would you need to look for a different explanation other than radiation? It doesn't make sense. A more obvious question is where did the radiation come from and I think Ryan has offered another possible explanation