She. The cases do not need to be frivolous. Exploitative behavior is all that is required. In this particular case, the defendant immediately removed the image when notified and offered a the photographer 5 times their usual licensing fee. That is an extremely reasonable resolution given there is no evidence that the defendant profited from its use of the image.

Attempting to further pursue the case after a reasonable settlement was offered is an attempt to use the court extrajudicially as a means to be financially punitive. That is the reasoning behind part (d) of rule 68 as referenced in the article.

Rejecting a rule 68 offer doesn't imply the offer was reasonable. Statutory damages mean that licensing fees are not necessarily the basis for damages.

Also, it's up the client to accept any offer, not the lawyer.

Again, given the defendant's compliance, reasonable offer, and the judge's obvious distaste for the whole ordeal, it is unlikely that they would be awarded anything but the minimum for both statutory and actual damages which would result in a smaller payout than the original offer.

Also, sure, the rejection alone may not imply that the offer was reasonable. However, the fact that this is apparently a common pattern of behavior, to the point that the judge (who has heard his cases and is familiar with his antics) decided to put their foot down, implies that the offer was reasonable and that Liebowitz is attempting to use the court for his own gain.