Users can get rights to projects in any of several ways:
Unlike some other rights, if a user has superuser rights to a project via all projects, the project's group or by owning it, that right is not overridden by assigning explicit rights here.
Clicking on a project brings up details for that project which permit access to tools, jobs, people via delegation and people via role. (Tool rights here do not inherit from rights to the equivalent global tool.)