"I don't trust their words."
Translation:Mi ne fidas iliajn vortojn.
Why do we use "al" in the other sentences then? Ex: "Mi fidas al ŝi". Isn't "ŝi" the direct object in that sentence too?
If a noun phase is the object of a preposition, then by definition it can not grammatically be the direct object of the verb (accusative).
Phrasal verbs (such as "to look something up" or "to believe in something/someone") employ particles that, on the surface, look like prepositions but aren't in this context.
But the fact that they look like prepositions are enough to trigger not-accusative, even if semantically it makes sense to say that the noun phrase is receiving the action of the verb.