I know exactly what you're saying and I've heard these unclear (veiled) HD-650's before. This pair is something special because it's crystal clear, yet very full sounding in the mids and has smooth treble. Not dark at all and no recessed sounding upper mids. There is a graph somewhere on Dr P's website that shows what mine would kind of look like if measured. Maybe I have that one. When I compared it to the HD-580 and 600 it sounded as if it had more extended low-bass, but just slightly.
You might find this strange but years back I had about 3 HD-650s and always was nit-picking about their stupid sound and didn't like them much. Too dark and muffled. I have the same amp and source around still. It wasn't just me getting used to the sound. I'm extremely picky.
This one is actually very close in sound to my (bass) modded Q701. Slightly fuller mids and slightly less treble. Obviously the Q701 has a larger soundstage and is more airy/spacious sounding. There is no real mid-bass hump on my HD-650. Nothing that sticks out really.
So anyway, i'm glad I gave the HD-650 another try. It all started when I bought an HD-580 for dirt cheap and found it better than the HD-600. It was the grills! It reduced the bass and sounded much more neutral and clearer. Probably not measurable.
Haha, maybe some HD-650s are just a complete fail with the Vali, but probably not.
I'll probably be keeping my HD-650 and Q701 for about forever since they have my favorite sound signatures.
Which amp do you like the HD 650 with?