I don't really know enough to challenge any technical arguments, but I do think that the headphone out and speaker out of integrated amplifiers can sound very different. Perhaps it's the circuitry. Hence, my Cyrus 6XP sounds quite warm and soft through the headphone out, not a description I'd use of the sound heard through three sets if speakers (which include my current PMC babies). Something must be happening with the output stages, and it may be the same with many other amps, hence the idea that headphone sockets on amps don't sound as good as headphone amps?
Just speculation, really. Like all things Hifi, one really has to listen in ones own system and without preconceived ideas to guage whether kit provides a worthwhile upgrade. On that, it seems we agree.