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There's another reason the tool might miss searches that you saw in your logs. Overture's tool often doesn't show the exact search. It will lump together singulars, plurals, spelling or punctuation variations and different word order searches and report them all as just one term. Example: blue widget, blue widgets, blue widget's and widjets blue will all be reported as searches for blue widgets. Overture's matching system shows your listing for such variations without you having to bid on them separately, so it doesn't bother reporting them separately.
Sooo ... Overture's tool is useful for setting up a term list on Overture, but it does not give enough details that you can use it to choose your best targets for regular on-page SEO.