Even the counterargument places the validity at 61%. This is from your OWN sources too.
I said that they weren't much better than chance. 61% isn't much better than chance. You also missed my second point, looking at the statistics of it.
Let's assume there were 100 people that were potential suspects, and only one killer. This seems to be a reasonable assumption. Taking the validity of the lie detector into account, let's use the numbers
P(fail | killer) = 0.61 (the probability that you'll fail the test given that you're the killer)
P(fail | not killer) = 0.39 (the probability that you'll fail even if you're innocent)
Then given the numbers of people, selecting any random person, we have:
P(killer) = 1 / 100
P(not killer) = 99 / 100
Putting it all together, we want to see how likely someone is to be the killer given that they failed a polygraph test:
P(killer | fail) = P(fail | killer)P(killer) / [P(fail | killer)P(killer) + P(fail | not killer)P(not killer)]
Plugging in the numbers, we get:
P(killer | fail) = 0.0156, or a 1.6% chance that the person was the killer given that they failed a polygraph. That's next to useless, given that selecting any random person would give you a 1% chance of having chosen correctly based on absolutely no evidence at all. If an individual fails a polygraph under these conditions, they still have a 98.4% chance of being innocent, only slightly down from the 99% chance they had before.
Let's make it stronger. Let's say that there were only 10 possible suspects, so now
P(killer) = 1/10
P(not killer) = 9/10
Now, P(killer | fail) = 14.8%, or ~5% more likely than having chosen a random person. Again, next to useless.