Don't you have to trust that all these are paid invoices? Yes, a user could provide an invoice you haven't included, which I don't see it ever happening, but anyway: How can the viewers verify that the invoices have been properly paid?

You can neither be sure even with a Bitcoin address. You can't know if the administrator hasn't changed the donation addresses before you visit the website for the first time. However, I really don't find a reason to lie. You're instantly becoming unlikeable if you lie for your own charity.