US AID doesn't spend the money, they send it to contractors to spend. They also contract auditors to make sure there are receipts for everything, etc. The problem is that many of the contractors are infested with Muslims and have been long before Hussein came along. Also the auditors usually work for the same shops and are paid extra to look the other way. Incompetent auditing (with a veneer of competence) is a highly lucrative skill amongst State Dept contractors.
While you are partly correct about the outcome of such spending, your assertion that USAID does not spend the money is a strange claim. It’s like saying a wholesaler runs the business of a small merchant to whom it sells goods.
USAID does indeed spend the money; the contractors are the beneficiaries.