There's no such thing as a lie detector test. If you're referring to a polygraph test, it doesn't actually detect lies but simply records a person's physiological reactions to a particular question. That's why results of a polygraph test aren't admissible in court, because they aren't reliable in determining whether or not a person is lying.
However, law enforcement routinely use them as a tool to at least tentatively and temporarily eliminate persons of interest....and these tests are routinely carried out by LE daily across the fruited plain.
Also, just asking the suspect to take a test and get a refusal is also a clue that the police tuck away in their heads.
If polygraph machines were of absolutely no value whatsoever, they would have been long gone as a crime-solving tool and would not even be manufactured because they would not be purchased.
I read the article but forget if this couple is still living and mentally alert. I wonder if they would consent to a test today.
IMHO, their tale is absurd and only mildly interesting.
Leni