For example; "No puppies were harmed in the making of this soda", implying that puppies are generally harmed in the production of soda, and thus casting the competition in a bad light.
Is there a name for this?
Is it maybe just a sneaky version of a straw man?
The suggestion/implication that soda's are made by harming puppies is exactly that: an implication, innuendo.
In this case, there's a clear suggestion that other soda makers are doing something that might be illegal, so I'd use the word innuendo or insinuation over implication here (as implication is a more general and neutral term anyway).
Some explanation-by-example thingy's:
Your example sentence implies the soda can it is written on doesn't harm puppies, where other producers do.
Those other manufacturers will react angrily, saying competitor NoPuppyPop's insinuations are completely unfounded, false and malicious.
The word malicious is why I'd say insinuation/innuendo is the word you're looking for
If you want a neologism for some reason: insanuation (insane + insinuation) is a common typo, or at least, so I hope. I did a quick google search:
Furtive lies and insanuation
All designed to tarnish my reputation
And devised by you without explination
Tell me why, why you spreading all these lies? mmm
Depending on whether it was written or spoken I would describe it either as a 'libelous or slanderous innuendo'.
But there are other terms that could be employed here: 'disparaging/snide/underhand reference/innuendo/implication'.
But I think the most important one to include is 'innuendo', which is something that is not spoken directly, but hinted at in an underhand way.
Ei incumbit probatio qui dicit is the ancient Roman legal concept that "the burden of proof is on he who declares, not on he who denies" is actually a better way of describing what is not happening when somebody is presumed guilty.
Regardless of any libel suit for damages in Common Law following countries like mine the judge (in the absence of minimum sentences), has Ex aequo et bono, or the Judge's right "to dispense with consideration of the law and consider solely what they consider to be fair and equitable in the case at hand." Under this logic though, it is still harder to prove that something did not happen then to assert it did.
That is what makes a successful libel case. Produce the dead puppies says the smart judge, except in the case of satire. This kind of satire has been used as plot development for many a South Park episode.
Eg. Kanye West and the "gay fish" episode.
