Definition:Argumentum ad Verecundiam
If the trustworthy person is also an expert in the field, and is free to speak their mind about the matter, then the argument has some validity. Otherwise, it generally does not.
That said, argumentum ad verecundiam can never serve as a (mathematical) proof, since no authority could ever be infallible.
If a well-reputed experimental physicist publishes a paper reporting results of an experiment, it is generally wise to trust that the experiment was performed competently and that the results were reported honestly.
However, if a well-known experimental physicist claims that certain plants are good for treating disease, one should not give much weight to the claims.