Ok, since I actually have a story in the first of this series, and just submitted my second for a future book, I'll speak up.
The "major NY publisher" is not one of the big six, but they are legit. We're also looking at another smaller, Canadian publisher who understands the they would be doing reprints of the first two books, then possibly taking over the series in the future.
Yes, all the authors retain the rights to their stories, but the antho as a whole, Alan has the rights currently, and if a publisher wishes to publish (or re-publish) he would sign them over to said publisher. Not unusual, especially in anthologies, or poetry collections. This is already understood.
These stories, in fact ARE carefully edited. Original schools, characters, plotlines and games. Really the only thing they have in common with HP is that they are young people attending Magick schools (yes, we use that spelling). Which isn't even really JKR's original idea; I think UJ has books about the magical education system.
We have a Ministry of Wizardry (but in the US is called the Federation of Magick, and there are all sorts of sub thingys. I have a list in an e-mail but I have to dig it out if you want to see)
No using any mythical creature JKR made up herself, like blast-ended skrewts. Normal mythical creatures are fair game.
Muggles - NO - Mundaes are people who are non-magickal.
Diagon Alley? Never heard of it! LOL No, we don't use any place that JKR made up.
This is kind of like fanfic, but with a major twist - it's not.
After having read the first book, I have to say that my own story, characters and Academy is probably the closest in style and story to HP, but again, my own creation. The others are SO different - like the reform school for wizards on the edge (of being arrested) or the school where all the students are 'corporeally challenged' - dead, but called 'reverberauts.' I don't think anyone would confuse them with HP. Personally I like the games they created, they're really interesting.
It's really quite clever, the way the stories weave together. We've even got permission to use the name of "Alivan's Master Wandmakers" -
the real company - to identify where all the wands come from. They've been very kind to us, even putting up wands as contest prizes.
Alan has taken great pains to make sure that we don't step on anyone's intellectual property. We're not even allowed to use owls as familiars, although she certainly doesn't hold the license on that. My own Academy's mail arrives by pixie.
If you go to the lulu listing you can take a peek, and decide for yourself. I actually submitted for fun, because it really was fun to write, and I enjoy doing it. They're for fans of that kind of story.