I believe this is because/relates to English being a 'stress-timed' language; others (such as Hindi) have 'emphatic particles' that emphasise the word they're attached to, and make more use of words like 'too' in 'I too would like some water' for this effect.
- I didn't say she stole my wallet. Tom saw it happen and he's the one who said she stole my wallet.
- I didn't say she stole my wallet. You're making up something I never said.
- I didn't say she stole my wallet. Maybe I suspected her, but I never actually said it.
- I didn't say she stole my wallet. Someone stole it, but I don't know who it was.
- I didn't say she stole my wallet. She took it, but for safekeeping after I forgot it at the restaurant.
- I didn't say she stole my wallet. I did see her steal a wallet, but it wasn't mine.
- I didn't say she stole my wallet. She stole my money but left the wallet exactly where it was.
It's a great example of how written speech doesn't capture all the nuance of spoken words. Well, italics helps, but hearing it makes a bigger impact.