Concluding our announcement of yesterday’s iPad trademark developments, I wrote that “Proview clearly hasn’t the means to afford a drawn-out, months-long legal battle with the richest company in the world.”

Apparently, they don’t have whatever common sense or rationality it takes to settle the case, either.

While we expected the beleaguered Chinese company to come to the bargaining bench with a realistic (or, at least, a marginally realistic) offer, it’s just not happening. Instead, Proview is said to be looking for an astronomical settlement in the billion-dollar price range. Billion. With a “B.” Ha!

Of course, the company might not have much ground to stand on. Its alternative course of action — a $2 billion US lawsuit on top of the $1.5 billion it’s seeking in Chinese court — is difficult to take seriously. Trademarks are, after all, tricky business, and Apple fully controls the US rights to the name.

Heck, Apple says it even controls the Chinese rights, having already transferred funds several years ago to purchase the mark from the very same Proview company that’s suing them now. If this bit of back-and-forth published by AllThingsD isn’t convincing enough, you can bet Apple’s reps have the necessary legal documentation to back everything up.

Proview might be able to get (low) double-digit millions out of Cupertino’s coffers to avoid further escalation, but that’s all. Apple’d probably buy the firm and gut it before shelling out much more cash than that. Well, maybe not, but professional spite in the face of blatant extortion and unhonored contracts is a very dangerous thing indeed.

Apple’s appeal for dismissal is pending.