Your proposed process (pulling a swab straight out of the box and using it only for one thing, then discarding) would actually tend to have more false positives, due to manufacturing anomalies / residues. For sampling media designed for re-use and used correctly, a track record of no positive signals is a much better predictor for no false positives than something being 'new'.

My heart rate actually goes up when I see a clerk opening a new box of gloves, putting them on and commenting that they got clean gloves. Huge recipe for a false positive. I want them to pull a new pair of gloves out of a box that is 90% gone. That means that they have had 45 tests where no one suspected the gloves were causing a false positive. @:-)

To put it another way... given the current equipment and procedures, and given my knowledge of the analysis technique, if I was in the ETD line and the TSO asked me, "This swab has been used 9 times and they were all negative, would you like me to use a fresh swab?" my answer would be "No, use the old swab."

Could a better process be designed? Probably. There are often compromises in a 'production' or 'real-life' environment that do not live up to the standards of peer-reviewed, publishable science. Would a process that meets laboratory-level scrutiny be cost- or time-effective? Almost certainly not.

That's all I can say on the subject. <shrug>

Thank you so much for that information, janetdoe!
I have a very serious question: Would it behoove you to insist that they first tested the new gloves that they pulled out of the newly opened box before they touched you or anything else at the checkpoint? (I am aware that that question might put you in jeopardy of the "That's not the way we do things at this airport!" retort, and possibly the "Do you want to fly today?" question.)

Do I smell a quality control engineer?

Well, that makes a lot of sense... IF instances of testing materials and gloves which are contaminated from the factory are greater than instances of cross-contamination from multiple uses in an uncontrolled environment where thousands of people per day walk by and the testers are careless untrained louts who wear their gloves to the food court, the bathroom, on smoke breaks, everywhere else.

Then yeah, I'd say used testing materials would be a better option than new testing materials.

You should always ask them to swab their gloves and get a negative test before they touch you. It is the appropriate protocol, and I have had a false positive once when they failed to do it; later they figured out it was the box of gloves. You can use that as your story if they argue.
Materials Science, but definitely some exposure to the topic. :D