Why did Naomi give that speech at the end of Metal Gear Solid?

Sure it makes for a nice ending to the game, but in character Naomi is probably the last person to make a speech like that. Despite the fact that she regrets her actions and the government of MGS 1 was very shady to say the least, they were going to lock her up for treason possibly for the rest of her days if they didn't execute her. She could maybe just be telling this to snake to get his mind off Foxdie but then she says "Don't worry, I'm going to choose life too".

Nice sentiment, but as far as she knew she didn't really have much of a future to look forward to. It seems odd she would try to be that optimistic about her own life.