At Gaia DR2 parallel-working meeting, Adrian Price-Whelan (Princeton) and I discussed co-moving stars with Jeff Andrews (Crete). Our discussion was inspired by the fact that Andrews has written some pretty strongly worded critical things about our own work with Semyeong Oh (Princeton). We clarified that there are three (or maybe four) different things you might want to be looking for: stars that have the same velocities (co-moving stars), stars that are dynamically bound (binaries), or stars that were born together (co-eval) or have the same birthplace or same abundances or same ages etc.. In the end we agreed that different catalogs might be made with different goals in mind, and different tolerances for completeness and purity. But one thing I insisted on (and perhaps pretty strongly) is that you can't have high completeness without taking on low purity. That is, you have to take on contamination if you want to sample the full distribution.
This is related to a much larger point: If you want a pure and complete sample, you have to cut your data extremely hard. Anyone who has a sample of anything that is both pure and complete is either missing large fractions of the population they care about, or else is spending way too much telescope time per object. In any real, sensible sample of anything in astronomy that is complete, we are going to have contamination. And any models or interpretation we make of the sample must take that contamination into account. Any astronomers who are unwilling to live with contamination are deciding not to use our resources to their fullest, and that's irresponsible, given their preciousness and their expense.