Wormtail in Gryffendor?

[Snape Uchiha]

I have always wondered why Wormtail (Peter Pettigrew) was in Gryffendor. Gryffendor is a house for brave people and it has been confirmed that Wormtsil is the most cowardly person in the Harrry Potter Universe.

He betrayed his friends to save himself. Hid from everyone for 13 years, ran to Voldemort because Sirius and Lupin were after him, and in general has always run away and tried to save himself.

Now some people might answer that a student has the right to request what house he is put in. However, I don't think one can be put into a house that is completely against his nature. While the Sorting Hat wanted to put Harry in Slytherin, Harry Requested to be put into Gryffendor because Harry was brave. I can't see the sorting hat just putting a huge coward in Gryffendor.

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[Cruciatus]

What about an extremely loyal person like Snape not being put into Hufflepuff? Or Snape not being sorted into Gryffindor, despite the amazing bravery he demonstrated throughout the series?
It's possible that Pettigrew changed after being placed into Gryffindor. While the Sorting Hat is magical, can it tell the future? It probably assessed Peter's nature at the time, and found Gryffindor the most appropriate house for him.