Bundy,

Your experience with this municipal agency is not that all uncommon in Texas.  I know, I am also a resident of Tx. and have already gone thru your experience.  It is a shame that agencies have applicants sign these waivers of non-disclosure why they are not hired, but have no problem sharing this information with other agencies.  
You really need to do two things.  First, consult with an attorney.  Failing this polygraph will haunt you for a long time.  Second, file an Open Records request with the city whose polygraph you failed to inspect your application, BI notes, and examiners report.  Remember, polygraph examiners are paid to get confessions and will stretch the truth themselves to get a departments business.  

I am very interested to find out what department failed you on the polygraph.  Certain, departments in the state are very well known for having very high failure rates on polygraphs.  The department in  my situation is in SE Texas.