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It looks like Tak is talking about a phrase match here in which case the potential exists for that phrase to show with other terms surrounding it also.
If "orange widgets" has become an established search, the phrase could show for i want orange widgets, bright orange widgets, etc.
Phrase Match ... If you enter your keyword in quotation marks, as in "tennis shoes ... possibly with other terms in the query... red tennis shoes
Essentially, what I'm trying to determine is if there is any way for me, as a searcher, to trigger only those ads that are set up to appear with exact match.
This gets to the idea of protecting ones trademarks. If the trademark is a phrase (as in more than one word, not an AdWords phrase match), it gets a little bit tricky trying to determine (quickly and easily) if companies are popping up due to a phrase/broad match, or if they are in fact using your trademark in their list of terms.
I think I actually found the answer in a thread from early last month:
Patient2All, it your answer there that tells me (I think) what I needed to know:
"...in your first post, I take it you're talking about the searcher's query, not your keyword list. google will strip all Boolean matching options the searcher uses plus any punctuation and quotes for adwords. It's a different story for the SERPs however. ...."