There are different type of dogs. Air-scent dogs don't need an article of clothing and apparently don't follow a specific scent of a specific human. So if those were air-scent dogs, then yes, they would just alert to someone being at the intersection, but not clear who.
"Air-scent dogs, on the other hand, work with their nose in the air. They pick up human scent anywhere in the vicinity -- they don't need a "last seen" starting point, an article to work from or a scent trail, and time is not an issue. Whereas tracking dogs follow a particular scent trail, air-scent dogs pick up a scent carried in air currents and seek out its origin -- the point of greatest concentration."
http://science.howstuffworks.com/zoology/mammals/sar-dog2.htm