gtk-doc-tools doesn't work when srcdir != builddir

gtk-doc-tools 1.16 is pretty broken when building with srcdir != builddir. A make distcheck fails when using it:

e.g.

ERROR: files left in build directory after distclean:
./doc/tmpl/layout.sgml
./doc/tmpl/greeter-protocol.sgml
./doc/tmpl/lightdm-gobject-0-unused.sgml
./doc/tmpl/session.sgml
./doc/tmpl/greeter.sgml
./doc/tmpl/user.sgml
./doc/tmpl/language.sgml
./doc/html/api-index-full.html
./doc/html/annotation-glossary.html
./doc/html/index.sgml
./doc/html/home.png
./doc/html/index.html
./doc/html/lightdm-gobject-0-greeter-protocol.html
./doc/html/lightdm-gobject-0.devhelp2
./doc/html/lightdm-gobject-0.devhelp
./doc/html/right.png
./doc/html/object-tree.html
./doc/html/LdmLayout.html
./doc/html/LdmUser.html
./doc/html/style.css
./doc/html/LdmSession.html
./doc/html/ch01.html
./doc/html/LdmLanguage.html
./doc/html/up.png
./doc/html/deprecated-api-index.html
./doc/html/left.png
./doc/html/LdmGreeter.html
make[1]: *** [distcleancheck] Error 1