Court costs can be much more expensive than the defendant can reasonably afford, even if they're likely to win. The copyright trolls take advantage of this by demanding less money than the court costs would actually sum up to, making it financially pointless to defend yourself rather than immediately pay up.
I agree that the grace period is also not a perfect solution, but I fail to see how anybody could consider the copyright trolls referenced in the article as anything more than predatory drains taking advantage of a legal technicality to drain money from innocent people. An honest typo regarding license text should not cost a person thousands of dollars, and copyright is one of the few places where it can do so, thanks to repeated lobbying and legal abuse.