Happy new year!
There are 2 most likely explanations:
1) Some flash players require the file url to end with ".swf". In the C1 3.2 the media url ends with "_swf" which causes the problem.
Workaround - either to insert the correct url manually, or to write a filter that would do the replacement "_swf" to ".swf"
The issue is fixed in the latest beta version http://compositec1.codeplex.com/workitem/1379
2) JWPlayer requires the attachment header, check if adding ?download=true or ?download=false to the media url, and see if it helps