If I understand the article correctly, the woman did not want to go through the body scan because she had a child she was holding. She requested that her hands be swabbed for explosives instead of going through the body scan - which apparently she's savvy enough to know she can opt for instead of the body scan machine (I didn't know that) and I wonder why she didn't opt for the metal detector w/ a toddler. TSA swabbed her hands as she requested and she tested positive for explosives.
Once she's positive for explosives she represents a threat, IMO. She presumptively has explosives on herself - so were did she hide them? They ask her to set the child down, which she does, but then, contrary to what she's been told to do, she picks the child back up. Her excuse is she was apparently unable to hand of her child to her husband because he for an unknown reason went to a different line (suspicious in and of itself as most family groups go through the line together.)
Now it is likely that the false positive was caused by a false positive (glycerin in baby wipes?) but she chose the swab rather than the body scan.
I'm no fan of TSA, but when it comes to someone testing positive for explosives I don't want them on my plane unless TSA knows for sure they do not have any.
The simple answer is choose the body scan next time.