Strictly speaking, Greenman’s example is of a company trying to generate alpha by deliberately parting from the index and trading around it at clever times. Tracking error without alpha does eat returns over time.
Alpha is of course the justification for taking on higher tracking error in active trading (this is just at the very low extreme of activity); you’ll want alpha > (TE^2)/2 (approximately) in order to be large enough to counteract the tracking error drag on perofrmance, and I guess if you are comparing Vanguard and other funds, you’d really just want alpha to be larger than one half the difference of the squares of the tracking errors (haven’t checked the algebra, but that’s my off-the-top-of-my-head guess).
It still doesn’t change the fact that higher tracking error will eat away at returns over time, the only real question is whether you believe there really is alpha generated and if it is enough to compensate for that.
So yes, if you have some kind of alpha generating process, and it’s large enough, it makes sense to have more tracking error.
Moreover, most index fund tracking errors are measured in basis points, and so the hurdle is probably pretty small before an some kind of alpha process makes sense.
If Vanguard has a tracking error of 6 bps, and DFA or iShares has a tracking error of 14 bps, then you you need an alpha difference from trading of only 0.8 of a basis point annually to justify the higher tracking error. That’s a pretty low hurdle, as long as you believe that the alpha is really there.
You’ll also recall that I said tracking error is “less important in the long term as long as it isn’t huge.” So this is all splitting hairs pretty finely.
Low tracking error on index funds is probably more important for marketing than for choosing funds, the difference fees are almost certainly going to have way more of an effect than the difference in tracking errors, at least for cap-weighted indexes, which have the advantage of self-reblacing without trading except for when companies are added or dropped from the index.