The Doctor's apparent death didn't "fool the timeline". It didn't need to do so.
The Silence wanted to be certain of killing the Doctor, so that he could never go to Trenzalore &, therefore, never answer the question being asked there ("Doctor who?").
The Doctor is a time traveller & the Silence knew it was possible that he might gain advance warning of the attempt to kill him -- as, in fact, he did. However, if his death were fixed point in time, he'd be unable to avoid it, even if he did gain advance warning of it.
The Silence chose Lake Silencio as the location for the killing because it was a "still point in time" (a term that has never been explained), which made it easy to create a fixed point in time.
The flaw in the Silence's plan was that whatever event occurred at Lake Silencio would be a fixed point in time, even if that event wasn't what the Silence thought it was.
The Doctor took advantage of this flaw by arranging for the Teselecta (wearing the appearance of the Doctor & with the Doctor himself inside it) to be the "victim" of the shooting. The fixed point was always the Teselecta being shot. However, the Silence thought the Doctor had been shot. So, initially, did Amy & Rory -- & the audience.
To provide the Teselecta with a way to leave the scene afterwards, the Doctor arranged for the "body" to be given a Viking-style funeral, being set adrift in a burning boat. As he eventually explained to Dorium, the Teselecta was unharmed by the fire (as were its inhabitants, including the Doctor). The boat, in contrast, did burn & that allowed the Teselecta to sink out of sight into the lake. Later, it simply walked out of the lake. (The Doctor never said whether it changed it appearance before doing so or took other precautions against being observed & recognised.)
In "The Impossible Astronaut", it was Canton who supplied the gasoline & who stated that it was "most certainly is the Doctor. And he is most certainly dead," to head Amy off when she almost gave the game away by suggesting that the victim was "a clone or a duplicate or something." And it was River (the older River, standing with Amy & Rory) who insisted on a swift cremation, ensuring that nobody had a chance to examine the "body" too closely.
In "The Wedding of River Song", when the younger River (in the spacesuit) tried to rewrite the fixed point by refusing to shoot, that refusal disrupted the timeline. She only relented & agreed to go ahead once she had learned that it wasn't the Doctor she'd be shooting but was instead the Teselecta (with the Doctor safe inside it). River shooting the Teselecta restored the timeline, because her shooting the Teselecta was the fixed point.
The Silence were fooled & so (temporarily) were Amy & Rory but the timeline wasn't. The timeline got the fixed point it needed -- River shooting the Teselecta.