the researchers could have simply selected 10 people with already white teeth.
You have the right idea about false stats, but this part is not quite right. It would not matter if they already had white teeth, because you describe a survey about whether people say the product whitens teeth. A better example would be if you mentions "participant bias" and suggest that they might survey only customers who have expressed satisfaction.
You gave an intelligent answer, but I think you know they are asking for a discussion of a specific area of research, such as the space program. Many people think we should have no space program because children are starving elsewhere in the world...
Others do not like global warming research, stem cell research... the list is long... Google around about controversial research funding.
What you wrote about here is just a desire to pull funding from studies with a weak design. Not only statistics, but many other studies, including experimental studies, can have flawed designs. We are looking for a research topic that should not be funded.