The phrase "false statements" refers to things that are said or written that are not true. It means that the information provided is incorrect or misleading. Full definition
There are state and federal laws about making false statements in official investigations, which would not be applicable to what you describe. (law.stackexchange.com)
Indeed, there are some situations where even false statements of fact that relate to a person's reputation are protected from liability. (law.stackexchange.com)
I do not promote my books by making false statements about, for example, their position on bestseller lists, or consent to anyone else promoting them for me in a misleading manner. (massimomarinoauthor.com)