Caveat: I don't think this is incredibly clear from the wording of the spell, so my answer will be subject to some semantic parsing.
No, that errata does not impact the effect of the Darkness spell.
The fact that "darkness" as opposed to "the effects of the Darkness spell" is listed as an example of a heavily-obscured area and that the spell description doesn't describe it as creating "a heavily obscured area" means that errata is kind of a red herring in this case.
The spell description says that a creature with darkvision can't see through it (which requires the logical leap that creatures without darkvision also can't see through it :) ), which means someone in the area of effect can't see out, since that would require seeing through some portion of the darkness.
A more grody scientific explanation would say that since "nonmagical light can't illuminate it," you can't see something unless light bounces off that thing and hits your eyes, and light that does do that would potentially be illuminating something in the darkness, so...no on that front as well (though if your game gets to the point of debating the nature of light itself, you might want to call it a day already).
The fog cloud spell says (emphasis mine):
You create a 20-foot-radius sphere of fog centered on a point within range. The sphere spreads around corners, and its area is heavily obscured. [...]
Unlike nonmagical darkness, other heavily obscured areas created by spells such as fog cloud do generally prevent creatures from being able to see through them (unless there is some feature, spell, magic item, etc. that allows them to do otherwise - such as the warlock's Devil's Sight eldritch invocation when it comes to the darkness spell).
The distinction is that nonmagical darkness doesn't involve stuff blocking your vision, just the absence of light in that area. If there's a light shining down at point A and another at point B, and there's a bit of mundane darkness in between (but nothing else obstructing your view), then nothing prevents you from seeing the light at point B if you're standing at point A. In contrast, if there's a bunch of fog (whether mundane or magical) between A and B, it may be harder (or even impossible) for you to see B from A.
(Note that this relies on a common-sense interpretation of nonmagical darkness - the rules don't draw such a distinction, presumably because they expect people to apply logic and common sense in understanding how regular darkness works.)
As such, a creature in the middle of the fog cloud would be unable to see a creature outside the cloud, just as the creature outside would be unable to see the creature within the cloud. If one attacked the other, the attacker's advantage from being unseen would be canceled out by their disadvantage from being unable to see their target.
Best Answer
Blinded vs "Effectively Blinded"
Blinded is a condition that is inflicted upon a creature. "Effectively Blinded" is a behaviour that a creature must follow even though it is not under the Blinded condition.
Immunity to being blinded only means that they cannot suffer from that condition. They can still encounter situations where objects and entities are obscured from their vision. In those cases the rules for targeting while blinded apply but only when attempting to target entities obscured by the fog.