There is a distinction between trusting a mathematical process and trusting random user "saurik" for example. I don't know you from hell, I would trust you to sell me lemonade. On the other hand, if you gave me a recipe for lemonade, that I could have the people I trust replicate for me. I might buy that recipe from you.
If you truly don't trust me in your example, you would be a fool to buy my recipe: you may have people you trust to replicate it, but it turns out that my recipe tastes horrible. You fundamentally cannot get away from having to trust the people whose first-hand accounts you are verifying.
