I think you grossly underestimate how hungry scientists are to prove each other wrong. This is part of how you build status to begin with. Yes, there are collaborative relationships, but there are also a great many adversarial relationships. There is no top-down hierarchy, so silencing dissent in this manner is unavailable.
I do think some degree of self-censorship occurs, absolutely. Are there biases, sure. But I find the claim that any given person is so influential in epidemiology that there is a conspiracy of silence lasting quite this long rather absurd.
California does not, in fact, require that home schoolers take a standard exam and we do not, in fact, have this data.
There are two states that require testing exclusively (other states have alternative options to an exam) and those are Oregon and South Dakota. To my knowledge no one has made a concerted effort to actually use these data to answer this question in a statistically valid way. One complication is that they are using these tests to force children back into public school if they do especially poorly. Given that some portion of these children are probably performing poorly due to more innate factors and not wholly educational neglect, this artificially inflates the home schoolers’ scores, because any low performing students are removed. But in theory, this can be modelled—it’s just that no one has done it yet.
The reality is we simply do not have any studies that show either is clearly better. Erik Hoel has more to say on this.