Being in NG+ or higher is essentially a requirement for having the black phantoms appear in your world. But this doesn't mean NG phantoms are impossible
, they're just incredibly more rare and either have more restrictive conditions, are randomized to appear inconsistently, or are a bug (unknown).
It's good to hear more confirmation on this from gravesworn here. Al10005 on youtube made a video that demonstrated how to have a friend spawn phantoms in your world consistantly. It worked every time on NG+ and higher characters, but always failed on the NG character. (Note that the servant doesn't have to be in NG+, but the 'infectee' does)
I've also done low level gravelording and messaged a good number of players who invaded through my sign if they saw phantoms in their world. I made sure they could see a new sign of mine to make sure they were 're-gravelorded', and also told them where they should be able to see them. None of the NG players ever saw the phantoms.
This was also sort of confirmed by Miyazaki in a recent interview:
I asked Miyazaki about some more specific ongoing aspects of Dark Souls play, such as the Gravelord covenant – is it true players can only see the black phantoms in NG+ and above?
“That is almost true,” Miyazaki almost answers. “In Dark Souls' design the position of enemies is fixed, so we could have intended to make the effect of Gravelord Covenant a new element seen in the second try after the game's ending. To be honest, I suppose I could have made it better.”
In short, it may be possible to see phantoms in NG every now and again, but it's inconsistant, rare, and unreliable. In NG+ and beyond, it seems to work consistently. So when people say NG+ is a requirement, it may not be the whole truth, but it's a good guide to follow if you actually want to spawn/ see phantoms. This renders low-level gravelording completely useless, and you should be at a level where the average playerbase starts hitting NG+ when you use an Eye of Death.