SCM Manager's Subversion component can't handle multiple, chained reverse proxies. In such a case, the HTTP request will contain multiple copies of the X-Forwarded-For, X-Forwarded-Host, and X-Forwarded-Server headers. It appears that SCM Manager only sees one instance of those headers.
To reproduce, set up two reverse proxies: proxy1 is client facing, and forwards to proxy2. Proxy2 forwards to SCM. Then perform an SVN COPY operation. SCM will give a 502 error, "Destination URI refers to a different server."
To work around the problem, add these two lines to the config for proxy1 (Apache):
ProxyAddHeaders Off RequestHeader edit Destination ^https://software https://scm early