Not yet, the Senate was still there and Palpatine was still the Chancellor rather than the Emperor. Even in the Empire era, he's not some personal protege. Tarkin was below the 13 Grand Admirals.
If they could show fake evidence Tarkin would not say "the sound doesn't work".
Grand moff was still huge considering it was apointed directly by the emperor to oversee territories. so protegé still fits very well.
And in the case of tarkin, not only he had several territories over his control more then any other grand moff he also had the deathstar in his control.
wich pretty much makes him in a position of huge power and responsability.
His apearence and role in the movie is actualy enough to warrant his importance