Difference a order word makes

This morning's Deseret News website has a story and a picture. The headline over the story reads:
Over 1/4 of US Homeless are Veterans
and the headline under the picture says:
Over 1/4 of Vets are Homeless

Of course, the story makes it clear that the former is correct. More than 25% of the homeless in the US are Veterans, while overall Veterans make up only 11% of the population.

Word order makes a difference!