Can Dual Link DVI do 4K at 60Hz? I've got a 4K monitor attached via Dual Link DVI. It does 4K, but only at 30Hz.

It does 60 Hz up to 2560x1440; anything above that is 30Hz.

Is that a limitation of DVI?
A single dual-link DVI connection can deliver up to 2560 × 1600 at 60 Hz. Achieving 4K at 60Hz requires two dual-link DVI cables, or DisplayPort 1.2 or HDMI 2.0.

So, yes, as you put it, that's a limitation of DVI.