Well, that's what he said...

On the music news on today's Radcliffe & Maconie 6Music show, the music news correspondent Elizabeth Alker was telling us about the Killers' gig being stopped halfway through. She said that from the start, the singer Brandon Flowers hadn't looked well and...

He started drinking what he said was a Chinese herbal remedy.

This caused Radcliffe and Maconie to ask her what it was then, if it wasn't a Chinese herbal remedy.

What? She just said it was!

See, what's happened here is that she explicitly said that the drink was a herbal remedy, but she implicitly communicated that she had reason to think that it wasn't. We can see this from R&M's response, and from the fact that the conversation continued and they said things like this:

Which you clearly think was a lie!
What reason have you got to doubt him?

It's handy, this implicature business. We can say all kinds of things without really saying them. There are two things interacting here, I think: contrastive stress and Grice's Maxim of Quantity.

The Maxim of Quantity is one of Grice's conversational maxims. These are principles that all speakers ought to abide by in order to keep conversation flowing smoothly. It gets interesting when speakers don't abide by them (which is a lot of the time), because we go through some complicated processes in order to keep the conversation from being derailed. We always assume that the person we're talking to is not flouting the maxims, so if they seem to, we work out a way in which they aren't. So if someone gives the apparently irrelevant response B to A's question, A will work out a possible meaning that makes it relevant and infer the intended meaning:

A: Do you want to go for pizza?
B: I'm on a diet.

B's being on a diet isn't an answer to the question, but A can work out that B means 'no' by assuming that B is being relevant, and therefore must be answering the question, and that the information provided must somehow have a bearing on the invitation. A works out how being on a diet might relate to eating pizza and fills in the gaps.

Here, Alkerpops (as she's known) seems to be giving too much information. She doesn't need to tell us that Flowers said it was a Chinese herbal remedy; we can work that out ourselves. By telling us too much, we have to assume that she's told us too much for a reason, and that it must be significant that he said that's what it was.

Secondly, she stressed the pronoun he. One job of stress in English is to contrast things. So you can say:

Sam wasn't the ring bearer, Frodo was. 

You're contrasting Sam with Frodo, in this case. If you don't mention two things, you can still be contrasting a thing, but you're contrasting it with either something from earlier in the discourse, or alternatively an implied contrasted thing. In our example above, he can only contrast with other people (things have to contrast with things of the same type), so she's implying that other people would say that it was something else:

He said it was a Chinese herbal remedy, but I think it was something a bit stronger. 

So we get almost the exact opposite meaning from what she said, with no difficulty, almost never any misunderstanding, and very consistent intuitions.