In the flashback, they showed Jigsaw's face,

Rating: 8/10 (20 February 2005)

Tapp should have known it wasn't Dr. Gordon, because according to the flashback, Tapp should have seen Jigsaw's face under the hood of the black and red robe.
Unless, the flashback was just for artistic effect and therefore shouldn't be taken as exactly what happened.
To understand what I'm saying you have closely watch the flashback at the end and you'll see that they show Jigsaw's face under the hood of his robe. He look likes he's looking at Tapp or his partner. Even so, Tapp should have seen his face. So, why do the writers make it like Tapp thought Dr. Lawrence Gordon did it?