Without more context, it's impossible to answer: if 'word' is a synonym of 'news', "word came that" is correct, but if 'word' is a synonym of 'instruction' "the word came that" - though rarer - would still be correct:
Word came that Friday was to be a holiday.
The word came that they should fire when ready.
But your search criteria allow both cases. In fact, you'd need a pretty sensitive search engine to make the distinction - perhaps something like SNOBOL - Wikipedia, the free encyclopedia (which I see is now rather old hat).
Besides, because of the subtlety of this difference, it is quite possible that in any instance a native speaker may choose the 'wrong' option, but 'wrong' reflects only a very low level of unacceptability to my ear.