Sorry, I only replied to the SF tracker. The language specs are vague but a very precise explanation for the "currently active exception" is given in the library reference for sys.get_info(). The language spec can be made precise just by copying or pointing to that text.
In other words, if we make explicit the implicit assumption that a bare 'raise' is indeed intended equivalent to
exc, val, tb = sys.exc_info() raise exc, val, tb
then the docs are already precise enough and CPython really implements that.