The fourth empowerment is not a direct introduction, it's a description of the Spiritual Master's experience as a pointing out instruction that gives powerful blessings, but not a mystical transfer of his complete experience.
A direct introduction is not a mystical transfer of a master's complete experience. It is a pointing out instruction. It does not transfer the master's realization (that is impossible), it communicates the student's own state.
Actually the word translated as "introduction" and "pointing out" is the same word i.e. ngo phrad.
Regarding Sakya Pandita, didn't he say that Dzogchen was not Buddhism?
Sakya Pandita criticized certain trends he saw in the Nyingma (much in the same way that Gorampa and Shakya Chogden criticized certain trends in Gelug), but he never stated that Dzogchen was not Buddhism, quite the opposite. He stated in fact that he had received Dzogchen teachings and respected them, as is stated plainly in his Analysis of the Three Vows. In fact, Sapan reserved most of his criticisms for the Kagyu school, spending very little time on the Nyingma school. After all, Sapan is a very important master for Vakjrakilaya teachings. Dzogchen is the ancestral teaching of the Khon family.