Why didn't Severus save this character?

Question

In the Harry Potter and the Deathly Hallows - Part 2 film adaptation we see Severus Snape crying over the dead body of Lily Potter. In this scene we can see that Harry is in the same room.

In the very beginning of the books, we are told that Harry was saved by Rubeus Hagrid:

‘No, sir – house was almost destroyed but I got him out all right before the Muggles started swarmin’ around. He fell asleep as we was flyin’ over Bristol.’

_{Harry Potter and the Philosopher's Stone, Chapter 1: The Boy who Lived.}

I haven't read the book in a while and my memory is not flawless, but I suspect the scene above doesn't happen this exact way in the book. If so,

1. What does actually happen? (book canon).
2. How is it that Severus wasn't the one who saved Harry Potter? (film canon).

Answer 1

Book Canon

I dug into the book (ePub version, thankfully) and found this excerpt:

And next, Snape was kneeling in Sirius’s old bedroom. Tears were dripping from the end of his hooked nose as he read the old letter from Lily. The second page carried only a few words:

could ever have been friends with Gellert Grindelwald. I think her mind’s going, personally!
Lots of love, Lily

Snape took the page bearing Lily’s signature, and her love, and tucked it inside his robes. Then he ripped in two the photograph he was also holding, so that he kept the part from which Lily laughed, throwing the portion showing James and Harry back on to the floor, under the chest of drawers...

_{Harry Potter and the Deathly Hallows, Chapter 33: The Price's Tale}

The chapter is told linearly (unlike the scene in the motion picture), so we know that this happens sometime between Harry leaves Privet Drive and Severus helps Harry into finding Gryffindor's Sword.

As it can be noticed, the scene is completely different and even happens 17 years later (in the book). I believe this was a needed change for the following reasons:

• The whole Lily's letter plot is left behind in the films.
• The scene was a vindication of Severus Snape's character; showing him ripping the photograph would have had a negative impact on the public.
• The scene is truly powerful; we see Snape bursting into tears upon seeing the lifeless body of his beloved.

Film Canon

Canonically, due to Fidelius Charm's nature, Severus should not have even been able to be there, unless Peter Pettigrew personally told him the location of the Potter's residence.

As @Deltharis has pointed out, this can only be explained through speculation.

Update: Fidelius Charm is inconsistently presented throughout the books, so anything is possible.

Personally, I'm gonna go with "Severus couldn't stay for too long without blowing up his cover".

Answer 2

Its accepted that Pettigrew was a double-agent, that the Order of The Phoniex knew nothing about and Snape was a Death Eater, so it is possible that Pettigrew could have told Snape what Voldemort was planning or had already done to the Potters, knowing that Snape had a deep hate of of James Potter. Snape having a secret love for Lily could have gone to the house without raising suspicion of Pettigrew and his fellow Death Eaters since they would have seen his as being loyal to Voldemort and going to the Potters to support him. Upon finding the destruction Voldemort caused it is reasonable to believe that Snape was that overcome with grief and despair at Lily's death that he could not bring himself to take or save Harry and he would have known that Voldemort's attack wouldn't have gone unnoticed by the Order therefore he quickly beat a retreat because he knew they would be arriving at any moment and that they'd obiviously take care of Harry.