Since your question is unanswered so far, I'll make some speculations. I agree that English doesn't allow adverbs to modify nouns.
If you changed "with" to "which has", it would be grammatical. The adverb is modifying the verb. That's possibly how these usages start. Equally likely, it's a variant of "with the precise inverse ..."
Either way the construct is not uncommon:
"One day you'll meet a girl with exactly the qualities you're looking for." 'with' = "who has". Or "with the exact qualities ..."
This is not the answer you want, but it might nudge your question up, and spark some more enlightening thoughts.
Student or Learner