As a default, GeoMedia's Export to Shapefile command outputs shapefile points as shapefile multi-point type geometries. Since esri's shapefile format cannot store both simple "single point" and "multipoint" in the same geometry field, GeoMedia exports shapefile points as multipoint. Exporting as multipoint shapefile format geometry ensures that any point geometry collections are not modified. If GeoMedia exported as single point, then any valid point collections would be either skipped or expanded to single points; thus as a default, GeoMedia exports shapefile points as multipoint shapefile format to ensure that any point geometry collections that might exist are not modified.
If you do not want to export your point geometries as shapefile multipoint format, a registery edit can be used to force GeoMedia to export as Point shapefile format geometries. See also this help topic for Exporting to Shapefile which states:
"By default, point feature classes with or without collections are exported as MultiPoint/MultiPointZ shape type. When DWORD value “AVExportPointAsPointShape” under the registry key HKEY_LOCAL_MACHINE\SOFTWARE\WOW6432Node\Intergraph\Applications\ is present and set to 1 (non-zero), the export point features are forced to be exported as Point/PointZ shape type, instead of MultiPoint/MultiPointZ."