To add to the obvious that has already been stated, the other obvious point is that it is probably pretty easy to pass a polygraph that you pay for.
Here is the guy whose company did Jone's test spinning some shit about polygraphs:
"The second witness to take the stand Tuesday was Peter Pierangeli, a polygraph expert in Albuquerque. He says although the test didn’t give an answer one way or the other, it still holds some value.
“It is a valid test. Why? We can still score it … can still solicit information from the test that is very valuable,” said Perangeli."
Basically this guy gets paid by legal teams to challenge the polygraph tests of other legal teams:
Polygraph experts testify in slayings case
Jim Fisher True Crime: The John Mayes Murder Case
You'd have to be a complete dipshit to buy into this.