does broad match override negatives?
Don't mean to take this thread off-topic, but yes - expanded broad match can do this. Your broad-matched 'spectacular widget' keyword may still get traffic even if you have 'spectacular' as a negative keyword. Google may match it to queries of 'astonishing widgets' or the like.
To the OP - I'm sorry, I'm not aware of why this would occur with Phrase or Exact match... it can't be expanded matching:
From Adwords Help:
Expanded matching only applies to your broad-matched keywords. This feature doesn't affect keywords you've specified as phrase matches (keywords surrounded by double quotation marks) or exact matches (keywords surrounded by [] brackets).
Sorry poster_boy, but my own experience is that negative keywords do effectively block the intended word, even with expanded broad match in play. The problem is usually that consumers will misspell a word that is supposed to be a negative, and if they do, their misspelled word does not exactly match the negative keyword. Negative keywords seem to be exact match only.
I think we've experienced the same issue. Evidenced by this statement:
I have had to include ... synonyms that G may like, but I don't want, even with broad match.
The moral of the story is... if you have a keyword that you do not want seeing the light of day - including a negative keyword of a word in that keyword will not ensure that keyword will not get exposure. The safest bet is to delete the keywords in question.
The safest bet is to delete the keywords in question.
Details aside, your efforts to prevent unwanted queries from matching to your keywords support that this is the case.