Since no answers were posted, I found the following here:
The Web server (running the Web site) thinks that the request submitted by the client (e.g. your Web browser or our CheckUpDown robot) can not be completed because it conflicts with some rule already established. For example, you may get a 409 error if you try to upload a file to the Web server which is older than the one already there – resulting in a version control conflict.
Someone on a similar question right here on stackoverflow, said the answer was:
I’ve had this issue when I was referencing the url of the document
library and not the destination file itself.i.e. try
http://server name/document library name/new file name.doc
However I am 100% sure this was not my case, since I checked the WebRequest’s URI property several times and the URI was complete with filename, and all the folders in the path existed on the sharepoint site.
Anyways, I hope this helps someone.