I don't know of infallibility in the dharmic context. Perhaps there are some paramparas where infallibilty is there, but I'm not aware of one. Definitely not a teaching in my sampradaya. Incredible wisdom, deep mystical realisation, insight, sure, all of that. But infallibility? That's just hyperbole at is finest.
"This person is NEVER wrong." Wow. Just wow.
For me, it's incredibly illogical. It's a person saying, "I tell the truth because I say that I tell the truth." It has no evidence to support it. Besides that, times change, each individual is unique, there are many colours to the world, and more. There is no absolute truth or one size fits all on a worldly level.
The Bahais do not accept blindly, the infallibility of Bahaullah or Abdulbaha.
The Bahai belief is solely through the investigation, and in my understanding, it relies on at least the following:
1. According to history Bahaullah and Abdulbaha did not study, and did not go to school, they did not have books to study, yet they had detailed knowledge of Traditions, histories, sciences, and holy books. Bahais see these as a sign of divinity. The history of Bahai Faith is fairly recent, and there are many historical accounts, which gives us a detail knowledge of days of Bahaullah and Abdulbaha, narrated by many people who lived at the time, summing to thousands of pages. There is nothing to refute the claim of Bahaullah as regards to His inner knowledge.
2. The woks of the Bab, Bahaullah and Abdulbaha, sums up to about 200 volumes of scriptures. No errors or mistakes could anybody proved in them. Their writings are available on internet.
3. The previous World Religions Traditions all prophesied about Manifestations of the Bab and Bahaullah, with many signs, such as the year, places and duration there Two would appear. All of these prophecies which are over thousands match with Them in Bahai View. There are many books written that explains details of these prophesies and showing they match the Bab and Bahaullah.
4. We know, for example Bahaullah lived in Persia, 19th century, and according to history, the people of His time were very cruel, superstitious, and fanatics. Bahaullah, among them, taught unity of mankind. Perfect democracy. He said they should vote and select their representatives, in locals and countries and worldwide, even though in His time they were kings and tyrants. He taught many new things as seen in His Writings, which clearly shows His Wisdom. He was also very powerful spiritually, and even He had many Enemies, yet, He could overcome them.
I only say these few reasons, just so it may be understood why Bahais believe Bahaullah.