That isn't entirely accurate. The problem isn't that the geometry is multi-part; it's that the geometry type is incorrect. For example, if the feature class is a Polyline class then you can insert any geometry as long as it implements IPolyline. It doesn't matter how many segments the polyline contains or if the segments are not all connected (i.e. it's a multi-part polyline). You can't, however, insert a Line, EllipticArc, CircularArc, or one of the other line type geometries. It has to be IPolyline.
You can check the geometry type expected by the feature class via IFeatureClass.ShapeType. Here is a breakdown of some common scenarios:
esriGeometryPoint - geometry must implement IPoint
esriGeometryMultiPoint - geometry must implement IMultiPoint
esriGeometryPolyline - geometry must implement IPolyline
esriGeometryPolygon - geometry must implement IPolygon