This isn't exactly accurate. One of the requirements for publicly traded funds (ETFs) is that they need to be "replicable", meaning that anyone should be able to read the methodologies (which are required to be public) and understand it and be able to come to the same final basket of securities at the same weights.

This, in practice, is very difficult even with everything public, though, due to a variety of differences such as data differences between vendors, "expert judgment" for unforeseen circumstances, and the mere fact that sometimes methodologies can be confusing, complex, or have vague language. Most indices, unlike the 500, are pretty hard on rules. The 500 is a rare index that is purely discretionary. They do give guidance on general guidelines, though.