So, two cases. Player A (A) and Player B (B)
B touches a piece. A sees it. B plays something else. A complains to arbiter that B didn't play the touched piece. Arbiter didn't see that B touched the piece.
B didn't violate any touch move rule. A complains to arbiter that B touched a piece and didn't move
So in case 1 A is telling the truth and B can deny it. In case 2 A is lying.
In these situations whose side does arbiter take? Assuming there are no 3rd party witnesses. How does the arbiter know who is lying and who is telling the truth?