"Deceptive statistics" is not a matter over which a person can be sued, so coming up with a court case will be hard. Fabricating data is not deceptive statistics – data fabrication would easily fall under the general rubric of fraud. Likewise, falsifying the application of a test is basically fraud (claiming to have performed an ANOVA on a set of numbers when in fact the results were just made up). We can group these two kinds of cases together as "falsified statistics". If I attempt to induce people to enter into a contract with me based on falsified statistics, I will have committed fraud. I would not be surprised to find cases where falsified statistics was an element of a fraud case.
It is also possible (and common) for legitimate data to be honestly run through the computation, where you get different results depending on which computation you run it through. Then the question is which of these computations is one legally allowed to report, and which others are you legally obligated to also report? It would depend, first, on who you are. Specifically, are you "just some guy", or do you have a professional obligation to a client? If I hire a professional statistician to sort out some data and the statistician treats 5 categories encoded with numbers 1-5 as a continuous variable, that is kind of incompetent and might be the grounds for a breach of contract suit. If I myself do that and then make a claim based on bad statistical thinking, I'm not liable to anyone for making that claim (even if I know that this is incorrect).
In order to sue a person for what you might call an unethical choice in the use of statistical methods, that person has to have some duty to you. Moreover, the choice has to be "clearly wrong", i.e. violates professional standards of that profession. Leaving aside fraud using falsified statistics, even technical incompetence is not actionable except in the context of a professional duty to a client. But, as a contractual matter, it is possible that a statistician could be held liable for damages to a client for incompetent application of the wrong statistical test. Your scenario suggests not just incompetence but deliberate cherry-picking for personal gain, so I don't know how to integrate that with the basic principles of law that I sketched.
In light of the recent edit, there are many cases of product liability where the company knew of a defect but did not fix the problem. Some of these no doubt involve misrepresentation of the product's safety, when the product has been subject to some safety test. In that group, we should exclude "scientifically wrong test" because e.g. tendency to explode is not calculated by testing pH.
"Bad statistics" could include numerous things, such as bad machines or bad procedures (the machine doesn't measure what it is claimed to measure; numerous flaws of the numerical analysis of the data). Again focusing on the contribution of statistical analysis, a person may have actual knowledge of sample bias but disregards that knowledge and took no steps to mitigate the bias. As I imagine you know, the world is rife with biased samples, many of them of the form "Oh, I didn't think of that". The manager making the decision about the sample may have a weak understanding of statistics, so may not have actual knowledge that the sample is invalid. If the analysis is outsourced to a statistician, the statistician may be unaware of the sampling problem. The court will ask whether the company took reasonable steps to test the product's safety, and whether an ordinary prudent person would know that cell phone interviewing biases the sample of the nation's population. A professional statistician may know that but Joe Manager probably does not.
I very much doubt that a failure to report confidence intervals would contribute to a civil action. Ordinary people never encounter a confidence interval, and consumers do not directly rely on confidence intervals to make decisions. However, there is an indirect avenue for confidence intervals in consumer decisions, via "unproven claims". If you claim that a product does X, in some cases you may have to prove that claim in advance (drugs for example). I suspect the best avenue for finding "knowingly bad statistics" in court will be snake oil claims. But snake oil claims are most likely disposed of administratively, without there being a lawsuit.