Why would he want to show the keywords? This would only create unneeded competition for him and give you free researched niches to jump into.
Since we've had ZERO input from the original poster, I'm guessing this was just a trolling post. My own personal interest to see the keywords is to see just exactly why it's not responding correctly. My big guess is that they're using a string of words that nobody searches for. Being number one for nothing, still yields nothing.
As for competing against them, personally I'd have no interest as the work has already been done. If someone is number one and complaining that they don't' get any traffic, why would I even bother to try and beat them on the same phrase. It's already "proven" that the search terms are useless at driving traffic for sales.
Now, if the user actually wanted HELP, I'm happy to help show where there might be a problem with the keyword phrase they're using, and a potentially better one to use, but again, my guess is that they are using something so specific or unsearched, that's the reason for the lack of performance.
My last point on all of this is that I would like to see proof. I'm very skeptical of someone saying that they have the number one position for ANYTHING, and then still need help. It's like a "hosting company" asking how shell works! It should never happen. I could claim to have cracked the Google code to rank any phrase #1, but without proof, nobody will believe me.
So it comes down to facts. I don't believe that this person has the number one position for a highly searched phrase and gets very few conversions. My site ranks #4 for a highly competitive term (4.6 million exact match results - 23.7 million broad match), another ranks #1 out of 20,300 exact match results and #1 from 2.09 million broad match... I get decent traffic, but then again, the terms are searched for also. If I was #1 for a term that nobody searched for, I wasted all my time.