A good argument could be made about the dynamic range bit. No DACs, especially early ones, actually had dynamic range which is as much as their number of bits would infer. A typical 16 bit DAC might have had actual resolution of something like 14-15 bits due to limitations of the time. Now if the "16 bit" card actually was capable of something like 14 bits of resolution, and the "32 bit" card managed to measure as having 15 bits of resolution, that's 6dB better, i.e. double the dynamic range, 6dB being twice as much.
Now, although I seriously doubt that hapless salesman had the sophistication to know about any of that, and he was no doubt spewing pure bullshit, he perhaps did have a point on at least the dynamic range bit.
The frequency response bit, not so much.....