HH Dalai lama is more Rime then anything, When he is universally loved by Buddhists of many sects its natural for him to present himself in a Non Partisan manner Gelug can no longer really lay claim to HH.
When I think of HH Dalai lama I think of Vajrayana in General rather then one sect in particular.
Abandoning Dharma is, in the final analysis, disparaging the Hinayana because of the Mahayana; favoring the Hinayana on account of the Mahayana; playing off sutra against tantra; playing off the four classes of the tantras against each other; favoring one of the Tibetan schools—the Sakya, Gelug, Kagyu, or Nyingma—and disparaging the rest; and so on. In other words, we abandon Dharma any time we favor our own tenets and disparage the rest.
Liberation in the Palm of your hand~Kyabje Pabongkha Rinpoche.