IIS8.5 with WebDAV only serves read-only files
Solution 1:
I don't have enough rep to comment, so I'm writing as answer.
Since you said that the setup works with Atlassian server and does not work with yours, what I would do to debug the problem is trace the HTTP communication and see what are diffferences in request/respnse data and headers.
For that I usually use smart sniff or wireshark.
This will not be helpful if either of those systems use SSL.