It sounds like someone sold NG a license for art that wasn't theirs. NG was also a victim here, it's not a lottery ticket for the artist.
I'm sorry the art was stolen, I'm glad they are trying to make it right by offering to pay ~10x his going rate.
It's interesting that the NG lawyer walked through the steps required for providing the $150k case. If you can convince him that those requisite facts are likely to be demonstrated, you will get a lot more money.
So I did some more research on the image in question. Honestly this sounds like something NG should have caught. I'm having a hard time imagining there's someone in NH who didn't recognize the image, and ensure it was properly cited. It's the cover image of a major issue, that should be something you get right.
If their process is so terrible they can't catch this image, then their process is willfully bad, and you can get them for $150k. It fails the De minimis test.
So I think that's the retort. Ultimately it's a bluff up until the point where you file a civil action. Tell them you'll take them to small claims and do it yourself if you must, there's definitely more money in it than $3k.
That said, I think NG does right by these letters. They have to start somewhere, and it's not by offering $150k up front. It was not aggressive and seemed genuinely apologetic. If they can give a plausible explanation of how this happened and what they are doing to ensure it never happens again you may find it wasn't actually willful.
Capitalism shouldn't suck only for the little guys.
Just ask yourself if National Geographic would let you dictate terms of a settlement because you claimed "someone sold [me] a license for art"?
If National Geographic doesn't like copyright law, they should come out publicly against it, not threaten a drawn-out lawsuit against the artist. On the other hand, now that they're obviously caught violating it, it's time to pay up.
Anything else is neither fair nor reasonable. Trying to get back to the simple licensing the artist offers _law-abiding_ licensees is not fair or reasonable.
National Geographic is welcome to go and pursue damages against their "someone" who sold it to them.
</sarc>
Since when did copyright infringement be made equal to theft?