From the UNHRC's Handbook on Procedures and Criteria for Determining Refugee Status under the 1951 Convention and the 1967 Protocol relating to the Status of Refugees
184. If the head of a family meets the criteria of the definition, his dependants are normally granted refugee status according to the principle of family unity.In other words, it is not automatic, like the case of Palestinians (and there is actually a further exception in 188 which states, "If the dependant of a refugee falls within the terms of one of the exclusion clauses, refugee status should be denied to him)! Many Palestinians would fall within the exception clause, which I discuss at the bottom.
187. Where the unity of a refugee's family is destroyed by divorce, separation or death, dependants who have been granted refugee status on the basis of family unity will retain such refugee status unless they fall within the terms of a cessation clause; or if they do not have reasons other than those of personal convenience for wishing to retain refugee status; or if they themselves no longer wish to be considered as refugees."
Cessation Clause (which EoZ mentioned):
113. Article 1 C of the 1951 Convention provides that:
“This Convention shall cease to apply to any person falling under the terms of section A if:
(1) He has voluntarily re-availed himself of the protection of the country of his nationality; or
(2) Having lost his nationality, he has voluntarily re-acquired it; or
(3) He has acquired a new nationality, and enjoys the protection of the country of his new nationality; or
(4) He has voluntarily re-established himself in the country which he left or outside which he remained owing to fear of persecution; or
(5) He can no longer, because the circumstances in connexion with which he has been recognized as a refugee have ceased to exist, continue to refuse to avail himself of the protection of the country of his nationality;
Provided that this paragraph shall not apply to a refugee falling under Section A (1) of this Article who is able to invoke compelling reasons arising out of previous persecution for refusing to avail himself of the protection of the country of nationality;
(6) Being a person who has no nationality he is, because the circumstances in connexion with which he has been recognized as a refugee have ceased to exist, able to return to the country of his former habitual residence
This is particularly interesting:
(3) Persons considered not to be deserving of international protectionArticle 1 F of the 1951 Convention:
“The provisions of this Convention shall not apply to any person with respect to whom there are serious reasons for considering that:
(a) he has committed a crime against peace, a war crime, or a crime against humanity, as defined in the international instruments drawn up to make provision in respect of such crimes;
(b) he has committed a serious non-political crime outside the country of refuge prior to his admission to that country as a refugee;
(c) he has been guilty of acts contrary to the purposes and principles of the United Nations.”
And now for the kicker:
A. War refugees
164. Persons compelled to leave their country of origin as a result of international or national armed conflicts are not normally considered refugees under the 1951 Convention or 1967 Protocol.22 They do, however, have the protection provided for in other international instruments, e.g. the Geneva Conventions of 1949 on the Protection of War Victims and the 1977 Protocol additional to the Geneva Conventions of 1949 relating to the protection of Victims of International Armed Conflicts.23
165. However, foreign invasion or occupation of all or part of a country can result--and occasionally has resulted--in persecution for one or more of the reasons enumerated in the 1951 Convention. In such cases, refugee status will depend upon whether the applicant is able to show that he has a “well-founded fear of being persecuted” in the occupied territory and, in addition, upon whether or not he is able to avail himself of the protection of his government, or of a protecting power whose duty it is to safeguard the interests of his country during the armed conflict, and whether such protection can be considered to be effective.
166. Protection may not be available if there are no diplomatic relations between the applicant's host country and his country of origin. If the applicant's government is itself in exile, the effectiveness of the protection that it is able to extend may be open to question. Thus, every case has to be judged on its merits, both in respect of well-founded fear of persecution and of the availability of effective protection on the part of the government of the country of origin.
For some additional points, I include some quotes from James Lindsay
"That is, UNRWA already grants refugee status to the children of refugees in Jordan, even though almost all of them are Jordanian citizens—this fact complicates any argument that matrilineal descendants in other areas should remain unregistered because they have citizenship through their nonrefugee fathers," pg. 25.
"Even UNRWA sometimes finds it difficult to remain coherent on the subject of citizens who are refugees. In a May 17, 2007, interview with Riz Khan of al-Jazeera, the commissioner-general stated, “Any group of refugees, until they can go home or until they are resettled or until they decide to integrate or take another nationality, they are, they remain refugees; their descendants remain refugees.” Yet, in the same interview, she noted that “the Jordanian government has given citizenship [to most of its Palestinian refugees], but that doesn’t take away the refugeehood; the refugee status remains.” Video of the interview available online " pg. 37.
"The roughly 414,000 UNRWA-registered Palestinian refugees in Lebanon have a significantly different status from their nonrefugee neighbors, but even there, some of UNRWA’s registered beneficiaries are likely citizens (given that Beirut granted citizenship to some 70,000 Palestinian Christian refugees in past years)," pg. 53.
"Nonetheless, with the increasing attention paid to women’s rights and gender equality (made a UN value by the UN Convention on the Elimination of All Forms of Discrimination against Women adopted in 1979)—and particularly since the May 1994 publication of Christine Cervenak’s influential article accusing UNRWA of “gender-based discrimination”—the agency has been embarrassed by its different treatment of the children of male and female refugees. In response, UNRWA began making a number of ad hoc adaptations, softening the effects of its discrimination against women married to nonrefugee men and the children of such marriages. With the adoption of the 2006 Consolidated Eligibility and Registration Instructions, nonrefugee husbands and descendants of registered refugee women are now entitled to apply for UNRWA services. Nevertheless, because matrilineal descendants still are not registered as refugees, the supposedly unequal treatment remains in a formal sense. Therefore, the pressure to categorize descendents of all registered refugees as refugees in their own right, adding tens of thousands of new “refugees” to the rolls, will likely continue," pg. 25.
So either Gunness is ignorant of the laws that govern his institution and the UNHCR or he's a liar. Maybe he's both.