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Your first two sentences might sound fine in theory, but practice is a different matter. I've used HD595 and HD650s for years with integrated amps (I'm currently using a Marantz PM5003) with excellent results. I've also listened to dedicated HP amps (LD Mk V, Cute Beyond, MF X-Can 2) and heard no difference whatsoever. The "fat resistor" you speak of isn't so fat (usually 220 ohms), and in my experience is totally innocuous, certainly with high impedance phones like the 650. As for the "cheap Ebay receiver", I was referring to quality brands like Marantz, Rotel and NAD of just a few years vintage, all of which are capable of very fine results. I wonder how many you've tried yourself?
I simplified a bit, but FYI, I have designed amps, listened to hundreds of them, and experimented with output impedance and speaker design interactions many times. What I said is correct, though perhaps I over-simplified. In audio engineering there are always twists that make the issue more complex.
Tom wrote a nice, non-engineer friendly explanation with charts that shows this nicely, for anyone interested.
http://www.avguide.com/blog/why-headphone-amps-sound-different-frequency-responseimpedance-issues
In slightly longer form: the degree of effect is simply a function of the headphone impedance curve, and the ratio of the output impedance to the headphone impedance.
The reason is simple: the output circuit is essentially a voltage divider, and as the headphone will have a bump in the bass range, high output impedance on the amp will cause the voltage to vary at the headphone, in the same places the impedance varies. The power that is delivered follows the function v*v/R (again, a bit of a simplification, as it's really Z not R, but that gets into more complex math). Since the voltage effect is squared but the impedance effect is linear, the higher the output Z *relative to the headphone*, the greater the effect will be.
A high-Z can like a HD650 is less sensitive to output impedance and will be pretty happy on any amp as long as the voltage and current are there. A low Z can will be more sensitive, unless it has a really bumpy impedance curve. That's why your particular choice of phones is less sensitive to the effect. But even with my 650, I can and do hear the difference on my Onkyo vs. my Burson, which are 5 and 300+ ohms output impedance, respectively. On the Onkyo, the 650 sounds muddy. My JH16s sound dreadful, but that is because they are multiple driver, low Z devices, so the effect is predictably greater.
So it's a bit more nuanced than I indicated, but for the majority of phones, which are low impedance, what I said is particularly relevant. Perhaps this may be why Sennheiser made the 650 Z so high... It's a less dependent of the amp output Z for frequency power specturm... Since this is a 650 thread I should have moderated my statement as it's at the far end of the impedance bell curve less effected by this.
Lastly whether you CARE or personally can perceive this is another issue. Some people probably really like the bass boost that results, especially if you're a bass head it may be just what you want. Others, like me, are sensitive to mid-bass and bass specturm changes and object to the effect. Some people really don't notice 1-3dB changes, but to me, they're glaring.