The process to allocate funding should be structured so that the opinions of the relevant experts are given great weight, even if the majority of the population disagrees. What I'm skeptical about is the need for secrecy.

As well you should be. What difference does it actually make if the media scaremonger a project? A group of physicists are still perfectly capable of getting together and conducting a quality analysis.

A government report that is going to be displayed to government officials and the public at large, written by people beholden to public opinion and the whims of government, will be written with those audiences in mind. Producing a quality government report therefore requires that it be kept secret and therefore not intended for non-experts. Emphasis on government. Producing a quality report doesn't require secrecy, as long as the people performing the analysis don't have to worry about being trodden beneath the blind elephant.