I am using PxGeometryQuery::sweep with PxHitFlag::eDEFAULT, PxHitFlag::eMTD flags, with small distance and zero inflation value. It returns false even when my capsule and the triangle mesh (I have also checked with heightfields) are overlapping, PxGeometryQuery::overlap returns true.
Sweeps do first a backface culling test for triangles. So if a triangle does initially overlap with the sweep shape that does not ensure it is always returned. If the triangle normal faces the same direction as the sweep it is culled. You can enable eMESH_BOTH_SIDES flag to get past the backface culling.