This is absolutely false.
No matter the source, let it be a HTC One M8, 3.5mm out of Surface Pro 3, or a great matching Valhalla2 or Bottlehead Crack, HD800 maintains all its characteristics, such as tight, extended bass (but low quantity/no bloat), detailed, accurate mids (albeit a bit dry) and simply unrivalled treble clarity and micro details (though a spike at 6KHz makes it unpleasant to listen to for a very long period of time in stock form).
It will always sound like an HD800, and definitely better than anything from the K7XX series. There is undeniable similarities between the sound signature of the HD800 and the K7XX series of headphones, but the different is noticeable at first listen. HD800 is noticeably the superior product.
You do not need $1000+ amps to make HD800 sound good. A Bottlehead Crack, Valhalla 2, or Torpedo amp will do just fine. It does need an amp that can deliver good power at 300-600 ohms (HD800 has a large impedance swing) and good voltage, but it does not need a very expensive amp.
Also another factor to keep in mind is product variation. I've owned 3 HD800 in the last five years and they all sounded exactly the same. The driver matching at Sennheiser Germany factory is scary good. No other brand or headphones will get you that.