Why in this example the mesh uses inexact constructions while the property map uses exact_construction?

[citystrawman]

Here's the cgal documentation for corefinement, it constructs a mesh using inexact_constructions, and a property_map using exact_construction:

typedef CGAL::Exact_predicates_inexact_constructions_kernel K;
typedef CGAL::Exact_predicates_exact_constructions_kernel EK;
typedef CGAL::Surface_mesh<K::Point_3> Mesh;
typedef boost::graph_traits<Mesh>::vertex_descriptor vertex_descriptor;
typedef Mesh::Property_map<vertex_descriptor,EK::Point_3> Exact_point_map;

and I do not understand why here Mesh uses Exact_predicates_inexact_constructions_kernel while the Exact_point_map uses Property_map<vertex_descriptor,EK::Point_3>.

Additionally, the Exact_point_map's vertex_descriptor is derived from Mesh, which uses
Exact_predicates_inexact_constructions_kernel , does that contradict with Exact_predicates_exact_constructions_kernel?