Here is the full text,
@Lanefan
So, notice that the heading- it's a subheading, under the "HIT POINTS" section, called, "Zero Hit Points". The first sentence ie explicit - when any creature is brought to 0 hit points (optionally as low as -3) it is unconscious. This is the specialized case for when a hit doesn't kill you (take you negative) but instead drops you to 0hp.
Why is this specialized and optional rule for zero hit points in the DMG? Look at the PHB section for damage:
Damage is meted out in hit points. If any creature reaches 0 or negative hit points, it is dead.
The specialized rule for unconsciousness is in contrast to the general principle that 0hp = dead that was well understood.
See, e.g., Len Lakofka in dragon Magazine #26 - June 1979 (killed is zero hp). This is the same as in OD&D, Holmes Basic, and Moldvay Basic.
I think that a lot of the confusion comes in from people who ended up playing a lot of 2e, and remember the "Hovering on Death's Door" rule, which is similar but different than the 1e DMG rule.