Is is true that you cannot fillet or chamfer the first segment of a polyline with the last segment of the same polyline?

True, you cannot fillet or chamfer the first segment of a polyline with the last segment of the same polyline.
AutoCAD is specifically designed for architectural planning and building constructions.

Chamfer is a symmetrical sloping surface at an edge or corner. It is an angled line that meets 2 straight objects or a sloped transition between 2 surfaces. Fillet is an arc that is created tangent between 2 objects.

In AutoCAD 2014, if you pick the first and last segments of an open polyline, an appropriate fillet or chamfer is then applied to close the polyline.

Used in engineering design and machining, a chamfer is a sloped edge, and a fillet is a rounded corner.The fillet and chamfer are transformation tools you'll find when using CAD. You need them to close gaps. The fillet tool has two end points tangent to an objects such as lines, rectangles, polygons, polylines, circular arcs etc. The tool places a fillet between adjacent sides of the object, including holes in polyines.

The fillet cannot work on objects that cannot be split or trimmed. A polyline rectangle that has a gap at one corner can't be closed with a chamfer or a fillet of zero length/radius. Your solution may be to break the polyline into lines and arcs.