At some point, you have to take someone's word that the software you are loading on your computer is "trustworthy", unless you're going to write it all yourself. And even then, how much of that code is going to be your own, and how much will be copied from elsewhere?
Free software isn't inherently more trustworthy, it simply moves the trust relationship around.
A physicist is an atom's way of knowing about atoms. -- George Wald