The idea is that for cash, the nominal rate is zero, so the real rate is (-inflation). Whereas for negative-real-rate bonds, the real rate is (r - inflation). Since r < inflation this is negative, but since r > 0, the magnitude is still below inflation.
The parent comment was maybe being slightly imprecise, but his core point isn't wrong that positive nominal rates means that your losses are less than inflation (whereas for cash they're equal to inflation).
But that misses the point that one can have negative (nominal) yields which give you very negative (real) yields. So it's not true that "they should always be bigger than inflation."
Right, it requires nominal r > 0. I think the parent comment point was that violating that condition is rare, but as you point out below, apparently it isn't.
What's the notional value of all negative nominal yield bonds? Surely it can't be that much? Though, if you expect rates to go ever lower, I guess you could argue that a negative nominal yield bond could be a good investment.
The parent comment was maybe being slightly imprecise, but his core point isn't wrong that positive nominal rates means that your losses are less than inflation (whereas for cash they're equal to inflation).