I had learned it this way: "tobie", like mnie, niemu, niej, nim, are only supposed to be used with the przyimki °przeciw° or °dziki,° whereas everything else °mi, ci, mu, jej, nam, wam, and im° are all used without przyimki, and that °tobie° and °jemu° are the variants able to be used at the beginning of sentences. In this sentence, it fits neither of those rules. Sorry for being a pain,, I'm one of those attentive to details people when it comes to langauges. I could be totally wrong, I just want to make sure.
You mean "dzięki" (thanks to)? "dziki" are "wild boars" :D Or the masculine adjective "wild".
It's true for 'niemu', 'niej' and 'nim'. If a given pronoun has more than one form and one of the forms starts with n-, that form is to be only used after a preposition.
"tobie" and "mnie" on the other hand, are simply emphatic forms. So "tobie" here is like "Why do they trust YOU?". Although then it would probably be better to put it at the end of the sentence to emphasize it even more.
And you're right about the beginning of the sentence, but it's not the only situation when they can be used. Anyway, the best option here would be "Dlaczego one ci ufają?".