Without emphasis, the sentence means, “I never said she ate my sandwich.”
The emphasis contains additional meaning not given in the sentence itself:
“[sentence] – someone else said it.”
“[sentence] – the supposed utterance did not in fact happen at all.”
“[sentence] – in fact, I relayed the sentiment via text message.”
“[sentence] – I said her brother did it!”
“[sentence] – she threw it in the trash.”
“[sentence] – the sandwich-deprived person was Ratel.”
“[sentence] – but she did eat my chips.”
Now the enhanced sentences, even without emphasis, match the various emphasized versions in meaning.
There’s a word for this gap (what’s conveyed in the words alone vs what’s conveyed with intonation and the like) in linguistics, but I’m having trouble summoning it.