I don't think pretending to be another entity should ever be permissible. The integrity of communications should not be compromised. Nor is that the intention of the parody-based fair use principles in IP law. The intention of the parody exception to liability is to give artists an opportunity to make fun of the high and mighty. Not to pretend to be them.
If we allow fraudulent messaging to come under the umbrella of parody protection, then this same exception will be abused by parties to malign their competitors. It will be difficult for consumers to know or trust the source of messaging, goods, or services.
It is no excuse to say no goods or services were actually produced, because to advertise a shitty bundle of goods in the name of another is enough to cast doubt on the good sense of that other.
A proper parody makes no pretense of its source. It proudly proclaims itself a form of protest. It doesn't dissemble and try to corrupt the flow of information/communication in commerce.
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If that's not "making fun of the high and mighty" I don't know what is.
You can also read more here: http://www.greenpeace.org/new-zealand/en/blog/shellfail-insi...
In my opinion this clearly classifies as parody.
Imagine the same standards being applied when someone is pretending to be you and maligning your name in public with foolish declarations.
Next, in the examples not an individual is "impersonated" but a faceless, anonymous corporation. I would have way more problems with the parody if an individual (independent to if I like them or not) would be impersonated or ridiculed.
If somebody makes similar fun of my employer, I would not mind at all.
So to adjust your example, if a group had a political complaint against Foster Farms and made a website claiming to sell obviously foul products, that would be a rich example of parody. "Damaging the brand" is pretty much the goal in an action like this.