Let me see if I can explain.
The HE-6 are very power hungry: They require watts and high current and more so for swings. Generally most headphone amps have smaller power supplies than any decent speaker amp. Now, most headphone amps can drive the HE-6 to good volumes, what they don't provide is the control or current, which good speaker amps do, as speaker amps are designed for much bigger transducers, and considering HE-6 are very inefficient, they perform similarly. Now when you drive the HE-6 from headphone amps and barely give them enough wattage, and not enough current, they are under powered; not under powered to mean they aren't loud enough, but to mean they are not getting the ideal power they need to shine. Now when they are under powered (as defined), they sound shrill and bright, with not enough control or slam in the bass. That is what happened when Tyll tried to run the HE-6 from the Teton and came to the conclusion he did.
Imagine high octane vs regular fuel. Both will drive the car and on both the cars will reach high speeds, but one of them gives the bigger engines the boost they require to accelerate faster.
It's really not about being a snob. The Anthem MCA20 that I currently have, which can be easily found used under $1K, drives the HE-6 better than any headphone amp I have tried (and I have tried many). I own the Ragnarok too so I've compared them side by side and concluded that it does not drive the HE-6 ideally, and it is more expensive than my Anthem. There are speaker amps like Bryston 2B which are even cheaper and drive the HE-6 better than headphone amps. When people own so many headphone amps, I don't understand why it's made to be a big deal that you add a speaker amp to the chain (which is much cheaper than a Ragnarok for example - you can add a speaker amp + schiit saga preamp easily under $1K). So if it's not about the money, why wouldn't you give the headphones they need? How is that being a snob/elite or whatever? Why would you spend so much more to get the best headphone amp when a cheaper speaker amp+preamp sounds better? I would understand if someone came to the conclusion that their headphone amp drives the HE-6 better than speaker amps, after having tried decent speaker amps which at least cost the same and are known to drive the HE-6 well, but why dismiss the idea when it's not about money at all and someone hasn't even heard a well driven HE-6?
Coming to a conclusion after trying it out is one thing, to dismiss the idea just because it's different and calling people snobs/elites etc is a different thing altogether. It doesn't hurt the wallet to try, it hurts the preconceived notions that are set about how anyone trying the HE-6 with speaker amps is somehow a snob.