It's not very hard to solve this problem. At work, we just have a bunch of small cubbies where everyone keeps their dosimeters. When you come in, you take it out and put it on; when you leave, you take it off and put it in. Occasionally people forget to take their dosimetry off, but it's not a big deal–it's extremely unlikely you're going to receive a significant dose outside of the facility (although you are constantly receiving a low-level radiation dose from cosmic rays, and, if you're below ground, from radon gas). I should mention that I work at a test reactor where the typical dosage is so low that the Federal Government doesn't even require us to track employee dose. I get more dose from flying cross-country several times a year[1] than I do working at the reactor. So, I don't know how dosimetry policy differs at power reactors.
Regardless, I think it would be particularly illuminating if there were false positives. Why not have employees who are concerned wear dosimeters constantly, and at the same time stick reference dosimeters near where they usually stand while a scanner is in operation. If their dose is roughly the same as that of the reference dosimetry, there's not much room to complain about the scanners.
The fact is we are being constantly bombarded by low-level radiation from cosmic rays and radon gas simply by virtue of standing on the surface of the earth. The level of radiation these scanners output is much smaller than that. Wikipedia[2] cites an article in the European Journal of Radiology that gives a dose range for backscatter machines of between 0.07 and 6 micro-Sieverts. For reference, the National Council on Radiation Protection and Measurements reports that the annual radiation dose from naturally occurring radiation is on the order of several hundred micro-Sieverts [3].
TSA employees have a right to be concerned, because they are involuntarily being exposed to it as a course of their job, without this being made clear to them when they were hired. If you're a traveler, you should be much more concerned about the radiation dose you receive on the plane than the one you receive from the scanner.
[1] Health Physics Society page on radiation exposure on commercial airflights: http://hps.org/publicinformation/ate/faqs/commercialflights.....
[2] https://secure.wikimedia.org/wikipedia/en/wiki/Backscatter_X...
[3] http://hps.org/documents/environmental_radiation_fact_sheet....