In my opinion, the DAC is the second most important component after the speakers - it is creating the signal you listen too.
Quality does in improve with price, but I don't know what price it stops being really noticeable.
Good DACs cost alot of money, and good preamps cost more than amp much of the time. I find volume control on the DAC chip to be much inferior to a preamp.
As for Amir, and ASR. As a person with "Scientist" in their job title, all I will say is that he is not doing science. Measurements are important because they can let you know if there is a design flaw, but measurements will not tell you what it sounds like.