Because he was correctly advised by legal counsel that poygraphs are so unreliable that the test results are inadmissible to prove guilt in just about every court in the country. His lawyer also told him that polygraphs are often abused by LEO as an interrogation tool.
From what I understand, he was willing to take a polygraph with his lawyer present (in case LEO used the polygraph to interrogate) and under the eye of a video camera, but that LEO rejected the offer. The real question then, is why were the police reluctant to conduct the polygraph?
Yup. Cops occasionally, ah, re-arrange interviews.
See this story (today's newspaper):
http://www.jsonline.com/news/state/apr05/322376.asp
Follows on another story, about a year old, were a man convicted of rape was set free after it was discovered that the local sheriff ignored ALL the evidence that the crime was committed by another person.
There's now a movement to require videotaping ALL police interrogations.