Since it's a book that only contains collaborations, ghost-written pieces, etc. and nothing at all that is wholly Lovecraft's I don't know why anyone would get an erroneous impression. Especially since the first thing you see after the TOC is a list of Lovecraft's rates for revisions and ghost-writing.
I'm afraid I have to disagree with you there, Teresa. While most of the tales in this book are indeed of that nature, this is something quite different. In all the other cases, both persons concerned had some say in the final version being submitted for publication, whereas Lovecraft was already dead when this was cobbled together by Miske, and therefore had no knowledge of the thing, let alone any input or opportunity to consent or otherwise. It isn't a ghost-written piece or a revision, it is a "posthumous collaboration" -- a questionable practice at best, even when the result is much better than is the case here. (Note: I am not entirely against such, but I am firmly of the opinion that these do need to be published as such, rather than as an actual collaboration or -- as was the case with this one for many years -- as the sole work of the deceased writer.)
In addition, this was not a finished piece of fiction, as were the other pieces in the book. It was an excerpt from a letter, written (as both HPL and those who witnessed his writing of letters have attested) with the same ease and fluent casualness as his speech; unlike his finished fiction, where he took almost infinite pains to find precisely the word or phrase for the effect he desired to achieve. And, though
the introduction may make it clear that these were all collaborations, ghost-written pieces, etc.,
neither the front cover nor the back cover copy does so (in fact, from the back cover, the
only one a reader is likely to realize is such is the Houdini piece); and that (along with the table of contents) is all many people will see until they have actually purchased a copy, given that the introduction is not available on the web, while the others are. Thus they are very likely to get the mistaken impression that this is "genuine Lovecraft".
Even those who may have a smattering of knowledge about HPL's revisions are likely to be led astray, given the general impression (fostered, with considerable truth in some cases, by August Derleth) that many, if not most of his "revisions", were in truth pieces of original fiction with, at best, a very vague plot germ or outline from the ostensible author -- and often not even that! In many cases, this is actually true -- "The Mound", "Medusa's Coil", "The Curse of Yig" and "Out of the Aeons" being prime examples.
Any way you slice it, the way it is handled here, "The Thing in the Moonlight" is likely to have quite a few people feeling they've bought a pig in a poke....
As to Joshi's methods of determining such... there were various methods used. Actual manuscripts for these tales are scarce; only two TMs exis (for "The Mound" and "Medusa's Coil"), which in both cases differ considerably from either the original publication or the later Arkham House reprintings, which themselves often differed from the original publication. This was only corrected in the editions released in the 1980s. There are also two AMs, ("Till A' the Seas" and "The Diary of Alonzo Typer"). In addition to these and the original publications (either in the pulps or, in no few cases, amateur journals), there is in correspondence (both by Lovecraft and others) and memoirs -- not to mention personal notes by such as Frank Belknap Long, who prepared the two typescripts mentioned above -- or the comments of the "collaborators", or clients, themselves --to indicate editorial alterations as well. Joshi has written quite a bit on this (rather arduous) process, not only in his note on the texts in the revised Arkham edition, but also in such pieces as "Who Wrote 'The Mound'?". (Incidentally, from what I've been able to gather, yes, the Wordsworth edition uses the old, highly-abridged Arkham House text of this one, rather than the restored version taken from the typescript....)