Voltage reference for DAC: is a reference really necessary?
My brain tells me that they're just trying to use an LDO as a low-pass
  filter. Why not just use a ferrite bead or inductor to block the HF
  noise coming from the rest of my circuit? Will this be less effective
  than using an LDO?


Take a look at the various graphs for ripple rejection and noise for the LP3985 and ask yourself if an FB or inductor will get anywhere near what the reference chip will do.

For starters, the LP3985 has an output impedance at DC of about 0.05 ohms and this rises slightly to about an ohm in the tens of kHz BUT, if you use a 10 uF output capacitor (or bigger) you will impose a much lower output impedance at those frequencies where the LP3985 is potentially weak.

How would this compare with an inductor or FB?

Output noise of the LP3985 is about 200 nV /rt(Hz) at 1 Hz and, ripple rejection is at least 60 dB at low frequencies / DC.

How can an inductor (of presumably moderate size) get anywhere near controlling noise and ripple that might come from your main power supply? What size of inductor could achieve this?

Most people like to use a voltage reference of course because you then have some kind of guarantee over what the DAC output voltage levels are. The LP3985 is a bit flaky in terms of initial accuracy and this is the only downside to using it as far as I can see.

Would that 3% accuracy be any worse than the accuracy and long-term drift of your main voltage regulator? Probably not and that is the scenario you get when using an inductor from that supply.

PS - don't put that inductor in the ground feed to your chip - it will cause more problems than any that potentially might be solved.