I don't know if it makes sense, but perhaps it would be convenient if I could copy a patch link from JIRA/Bugzilla, and enter that link URL into the "Apply patch" dialog.
Maybe just rename "Patch file name" to "Patch file path", and support http: protocol without any additional UI?
Then again, my experience with working with patches is limited, so there might be better UI ideas available.
If the system clipboard contains a string that looks like HTTP url, prepopulate relevant field on dialog using this value.
Omea reader has this feature, and it's very 'fluent'