edit: nevermind, see the bottom
There's no upper limit on headphone impedances in terms of what amplifiers can do. That's just some cruddy audiophile myth that needs to die. Higher impedances are easier to drive, except if you're talking about necessary volume. If an amp can run fine into 100 ohms, it will do just great into 300 ohms, 600 ohms, whatever else higher.
A lot of receivers will have bad headphone outputs because that's not a priority in the design. If the implementation is unsuitable for headphones, then you get unsuitable performance. If they're tapping the speaker amp with a resistor, that's the laziest and lowest-quality design. Other receivers may have some kind of dedicated cheap circuit for the headphone output, which may be much better but of course not comparable to better dedicated headphone amps.
The loudness is just determined by the power the headphones get and the sensitivity, generally listed in sound pressure level (in dB, referenced to 0 dB being the quietest things humans can hear) per milliwatt of power input. Sometimes it's given per volt of input. Power is voltage squared divided by impedance, so if two headphones had the same sensitivity (same loudness at a given electrical power input) but different impedances, then the higher-impedance headphone would need higher voltage to get the same amount of electrical power and thus sound pressure level. Hence why in practice, many high-impedance headphones are not loud enough on many portable or cheaper sources, which are limited in output voltage.
ATH-M50 are relatively sensitive, needing only 0.041V for 90 dB SPL, according to InnerFidelity. For a very loud 110 dB SPL, that only requires 0.41V, or 4.4mW. ATH-M50 also notably has a very constant impedance over frequency, so you wouldn't get big FR shifts using that. These would be some of the ones that would suffer the least from the issues I pointed out earlier, if the output impedance is really 680 ohms.
On second thought, the 0.3V max may be into 8 ohms and not into infinite ohms? That makes more sense. So about 26V output with 680 ohms in between the output and the headphones? With 38 ohms ATH-M50, max output would then be 1.35V or so, which would be really loud for those headphones and would make sense with what you're hearing.
edit2: nevermind, looks like probably 25-26V peak so divide that by sqrt(2) for around 18V (rms sine wave) max. That would still make the ATH-M50 plenty loud, so this is making sense. I was wrong earlier about output level if my interpretation in this post is correct--it will be loud enough for most headphones.
With HD 598, which has a huge difference in impedance over frequency, expect a huge boost in amplitude at frequencies where the impedance is relatively high. Or more accurately, the other frequencies will be attenuated by a much greater amount.
ATH-M50 impedance vs. frequency (left), HD 598 impedance vs. frequency (right)...note log-log scale