How can one ensure that the person requesting charity is deserving, especially when they present documents proving their need?

The one who gives charity must investigate where their charity goes by searching for those in need. If someone comes forward with proof of their need, and the default assumption is that Muslims' affairs are sound, then one should act upon what is apparent. This is because searching into inner intentions is not required, and because an error in giving is better than being correct in withholding. The reward for charity is based on the purity of intention.