This Bloomberg article talks about the difficulties certain Pacific nations have had with taking measures to restrict imports of unhealthy food, without violating WTO rules. The focus is on Samoa's accession committments related to imports of turkey tails:

After a 13-year wait, the South Pacific island nation of Samoa should win approval to join the World Trade Organization next month after dropping its ban on turkey tails. The WTO welcomed the nation, with a population of about 193,000 (a bit more than Knoxville, Tenn.) once Samoa agreed to end its ban on the fatty poultry scraps and impose import tariffs instead. That’s good news for U.S. turkey farmers, who will regain a market for the low-value trimmings that often end up in pet food, says Roman Grynberg, a trade official for the Pacific region until 2009. For Samoa, one of the world’s most obese nations, the deal is a mixed blessing. “These are the contradictions we have to face—where health is compromised for the sake of trade and development,” says Palanitina Tupuimatagi Toelupe, Samoa’s director general of health. The U.S. food industry sees the issue differently. “We feel it’s the consumers’ right to determine what foods they wish to consume, not the government’s,” says James H. Sumner, president of the USA Poultry & Egg Export Council. Samoan negotiators defend ending the ban as the only way to enjoy the increased trade and lowered costs of imports that WTO membership confers. “It filters down to the normal customer who will now have access to a wider variety of goods,” Namulauulu Sami Leota, president of the Chamber of Commerce, told the Samoa Observer newspaper. Reaching an agreement “was not an easy task,” added Namulauulu, who was involved in the final talks. Keith Rockwell, a spokesman for the WTO in Geneva, says the ban “was an issue on which Samoa took quite a tough line.”

As a general matter, it seems to me that it would be very easy to come up with domestic regulations that restrict unhealthy foods, without violating trade agreements. At the same time, I'm not sure exactly what accession commitments Samoa has made on this issue. Here's a summary from the WTO's announcement about the Working Party's adoption of Samoa's membership package:

Samoa would within 12 months of its accession eliminate the prohibition on the importation and domestic distribution of turkey tails and turkey tail products in Samoa. As transitional measures, a domestic ban on the sale of turkey tails and turkey tail products would be in place and an import duty of 300% would apply to the imports. This is to allow time to develop and implement a nation-wide programme promoting healthier diet and life style choices. After two years, the domestic sale ban would be lifted and the import duty would be reduced to 100% or replaced by another tax regulation or by recommendations from the programme. From the date of accession, Samoa would not introduce, re-introduce or apply quantitative restrictions on imports, or other non-tariff measures such as licensing, quotas, prohibitions, bans and other restrictions having equivalent effect that cannot be justified under the provisions of the WTO Agreement with the exception of those related to the import ban of left-hand drive vehicles, automobiles older than 12 years and the domestic sale prohibition of turkey tails and turkey tail products (see sections above for Samoa’s commitments in relation to these exemptions).

Based on this summary (as far as I can tell, the full accession documents are not public yet), I would say there is some flexibility to take measures that restrict turkey tail consumption, if that's what Samoa wants to do. But I'd want to see the actual text of the accession commitments before reaching a final conclusion.

At the same time, it does seem clear that U.S. turkey tail exporters lobbied hard to get their products into Samoa, and were able to obtain some sort of market opening commitment. Here's a little more about turkey tails: