For anyone who cares whether their beliefs are true, 2 has a burden of proof as well.
Because people who care whether their beliefs are true ask themselves questions like "how can I tell whether my belief is true or not?" and then seek out the answer.
If you haven't bothered to demonstrate to yourself that your belief is true, then you aren't that concerned with believing false things.
I still "believe" that the only reason TB started this whole thing about beliefs vs. claims is that she wanted to have an excuse not to have any burden of proof. But what does a person that believes in a religion do when asked, "Why do you believe it?" And she has said that she has looked at the so-called evidence and has proven it to herself that the claims of her prophet are true. So, she might as well claim it... Baha'u'llah, to her, is a manifestation of God. Why? Because, she says, his character, his mission and his writings.
Ah yes, but I forgot, she can't "prove" it. And she can't prove God exists. She says there's "evidence" but no "proof." With no "proof", she says she can't "claim" it. Except here's a
Baha'i article that claims there is proof.
In the Baha’i teachings, we find three varieties of proofs for the existence of God—”rational” (logical, scientific) proofs; “scriptural proofs from the Old and New Testaments or the Koran;” and “spiritual proofs.” There are also sensory and scientific proofs for the existence of God, and the first essays in this series deal with those proofs.
The Baha'i author of that article also wrote some books about "proofs".
Peter Terry is an independent religious scholar, musician and educator. He is the author of A Prophet in Modern Times (a biography of the Bab); In His Own Words (an autobiography of Baha'u'llah); Proofs of the Prophets (a compilation and commentary on 40 proofs of prophethood); Companion to Proofs of the Prophets; Proofs of the Prophets--Lord Krishna; and Proofs of the Prophets--Baha'u'llah.