I've had this headcanon about why this scene happens the way it did for awhile now, so I finally decided to get it out with a short drabble. None of the characters belong to me, of course, and the text in italics is directly from Harry Potter and the Sorcerer's Stone. I am in no way claiming that section of text as my own.
"So, we're agreed that Mister Potter, Mister Weasley, and Miss Granger will each get sixty points for their bravery in protecting the Philosophers Stone," Minerva said to Albus after he returned from visiting Harry in the hospital wing. All the teachers had agreed - even Snape, reluctantly - that their actions were deserving of winning Gryffindor the House Cup.
Suddenly, a house elf apparated into the headmaster's study. "We is needing you in Gryffindor tower, Professor," the elf said. "Mister Longbottom has been found hexed on the floor."
Minerva sighed. "Thank you, Pip. I will tend to Mister Longbottom." She stood up and left quickly for the Gryffindor common room. It was merely moments later when she returned. "Petrificus totalis," she said crisply. "Mister Longbottom tried to keep Mister Potter and his friends from going out after curfew. I'm afraid Miss Granger is not a witch to cross."
Dumbledore's eyes twinkled. "Ah, how unfortunate for the young man. Still, I think now you can cease to worry about his fitness for Gryffindor house." Minerva nodded. "Actually, Minerva, I have an idea. Allow me to dispense these last minute house points at the feast, if you will."
Minerva eyed him suspiciously. "I suppose it does not matter who gives out the points," she says slowly. "Very well, we can wait until the feast and you can announce the house points."
Albus felt Minerva's eyes on him as he awarded Mister Weasley and Miss Granger fifty points each. He couldn't help a small smile, and gave Mister Potter the previously agreed upon sixty points. A tie now, between Gryffindor and Slytherin.
"There are all kinds of courage," said Dumbledore, smiling. "It takes a great deal of bravery to stand up to our enemies, but just as much to stand up to our friends. I therefore award ten points to Mr. Neville Longbottom."
The roar from Gryffindor table was deafening as Neville disappeared under a pile of cheering students. Albus looked at Minerva, smiling. With time and encouragement, he thought to himself, Mister Longbottom would become a very brave and talented wizard indeed.