Sphinx's latex writer needs fixing to match the html output more closely. This issue will occur also if you use regular citations in Sphinx: it has nothing to do with sphinxcontrib-bibtex per se.
Users of sphinxcontrib-bibtex are of course the most likely ones to encounter this problem. I've created an upstream ticket for it: https://github.com/mcmtroffaes/sphinxcontrib-bibtex/issues/48
For now, a workaround for this issue is to create a rubric only when html is generated:
.. only:: html
.. rubric:: References
.. bibliography:: refs.bib