Um, the "shill for money" program got busted, so don't wait by your mailbox for your $2500.
Yes. The American Egg Board is an FDA-established entity specifically to market an agricultural commodity to consumers. It's intentionally a joint effort between the industry and the agency, so bias is inevitable. It's advertising.
A lot of the sturm und drang on this page, and in the media, is the unfairness of it, but honestly, "unfair" is to be expected from advertising.
Real opprobrium is called for, though, because this attack marketing campaign appears to violate the actual regulations with respect AEB advertising:
(e) No advertising or promotion programs shall use false or unwarranted claims or make any reference to private brand names of eggs, egg products, spent fowl, and products of spent fowl or use unfair or deceptive acts or practices with respect to quality, value, or use of any competing product.
(2015 Code of Federal Regulations, Title 7, Subtitle B, Chapter XI, Part 1250, Section 1250.341(e); emphasis added)
Now, lawyers could make shedloads of money arguing about the legal boundaries of "unfair or deceptive acts", but I suspect that if you take the AEB's acts to a judge (assuming you find one who hadn't already been bought out by the industry), he would assess that the attack marketing and astroturfing would qualify. Certainly, with all the publicity, the bureaucrats responsible for administering the government part of the program (and enforcing the rules) would be encouraged to see it that way. (Although bureaucrats are also known for occasionally doubling down on stupid and digging in. At least, until the lawsuit, after which the "no fault admitted" settlement puts the entire issue to bed.)
"tl;dr:" The point that the AEB attack campaign violates the intent of the controlling regulation is supportable, and is the legal sticking point in play. The AEB attack campaign is also unethical, but then again ethics is what makes loser business lose. Winner businesses don't let themselves be burdened by anything that doesn't have an explicit and costly punishment for violating.