This came up a little bit in the ID special as well, specifically that the film Ransom came out just before JBR's death and could have been the inspiration for the RN. That movie was released in theaters 11/08/96, so if PR's assertion is truthful that they never went out to see movies but rather watched them at home after video release, then it wouldn't jive (and yes, it did take something like a year between theater and VHS release back then!). However, even if they hadn't watched the movie, they were likely aware of it and its popularity at the time.
A quick watch of the trailer draws some eerie similarities:
[video=youtube;mebIhXK8srA]https://www.youtube.com/watch?v=mebIhXK8srA[/video]
A self-made man, interest in aviation, wealthy family, interviews with the media, some of the RN wording, etc.
There's an interesting thread here about connections between JBR's death and movies:
http://www.topix.com/forum/news/jonbenet-ramsey/TPC0N4J80QQ25C38U
I personally find the most striking similarities between Dirty Harry and the RN. It has been reported that Dirty Harry aired on TBS in Boulder on 11/29/96, but I can't find anything to officially substantiate that.
IMO, the suspiciousness of JR's and PR's behavior is the biggest and most obvious indicator of their guilt. If there was staging and then cover up, then what do you use to determine the things that you should say and do? If you've never written a RN, staged a crime, dealt with police, or done TV interviews, you are going to default to examples of those things portrayed in the media. JR and PR thought they were saying and doing all the right things, but IMO they were so obviously cloned from pop culture and disingenuous that their efforts served to increase suspicions of their guilt.