The object of a preposition is an indirect object. The accusative marks the direct object.
I give the ball to you.
"ball" is the direct object of "give". It's what's given.
"you" is the indirect object of "give". It's the recipient of the given thing (the ball).
So it's the difference between "I thank you" and "I give my thanks to you".
While it is quite true that in Esperanto all prepositions govern the unmarked (non-accusative) case, aaronalbre's question wasn't about that. It was why fidi has to be part of a verb+preposition phrase -- fidi al -- in the first place. Why not just Mi fidas vin?
I see examples of both structures in Esperanto texts: e.g. Mi povas fidi vin and Mi povas fidi al vi ; Ĉu vi fidas min? and Ĉu vi fidas al mi? Is there any real difference in meaning?
Isn't this really one of those cases where whether or not one uses a verb+preposition phrase (and, if so, which preposition) depends very much on the influence of one's first language? Prepositions are always tricky beasts to pin down in regard both to their meaning as between one language and another and to the need or non-need for their use at all. One of the "flexibilities" of Esperanto is surely that it allows for such variations.