I read the definition of 信用:
人の言動や物事を間違いないとして,受け入れること
I have looked around a bit and found What does verb+とする mean? but it only covers "dictionary verb form + とする"
This one is after a negative «ない», so I wonder if they are different.
So far I understand the sentence as «to accept the word and «thing» of a person and do so with no doubts».