Why do they have to take your word for it? if you present a few forms of id (drivers license, etc) can't those be checked against a central DB?

is someone forging physical ID cards and also getting them real numbers somehow?

The people who have to do the check (businesses and landlords) don't have access to the system to check those numbers, or any training on what a real identify card or passport looks like.

A relative had this problem when renting out a spare room. How was she supposed to verify the Colombian passport shown to her?