This claim is… questionable… at best.
It all depends on what you mean by “producer”.
The claim is based on data from Bowker – the one and only place to get ISBNs in the United States. Anyone else who offers an ISBN – me, Smashwords, Google – has bought those ISBNs from Bowker. When the ISBN is assigned to a book, then you have to tell Bowker about it.
Smashwords offers free ISBNs (as does CreateSpace, who ranks right up there in the report when you include print books). It seems like a great deal – individual ISBNs are horribly expensive. The per-unit price goes down a lot when you buy them in bulk, but you have to have the cash up front.
Assigning an ISBN to a book makes you the “publisher of record” – whether the person who gives you the ISBN had a damn thing to do with actually creating the work or not. And by my lights, that doesn’t make you a publisher… or even a “producer”.
Of course, Bowker does have something that nobody else really has. They have an accurate record of who has bought ISBNs, and who has assigned ISBNs to books. So we can definitely say:
Smashwords is the #1 assigner of ISBNs to Indie eBooks in the United States.
That’s actually a fairly impressive thing. And the data reveals something else as well:
The top four entries in that table are Smashwords, Luly, AuthorHouse, and Xlibris. Both AuthorHouse and Xlibris are part of the uber-vanity-press-scammers Author Solutions. Author Solutions is so scammy that they’re the subject of a class action lawsuit (yes, despite them being owned by RandomPenguinHouse).
What’s a little harder to see is that Author Solutions’ ISBN assignation numbers are shrinking. And that’s from 2012 – before the class action lawsuit really got underway. Whilst it’s correlational, this seems to imply that Smashword’s gain is Author Solution’s (via AuthorHouse and Xlibris) loss. Smashwords is a distribution platform, and has helped a lot of indie authors get to markets they otherwise wouldn’t have. I believe it’s clear from this data that the availability of platforms like Smashwords means that authors have more options and more information, making it harder for scammers to run their scams.
By my lights, that’s a damn fine thing for Smashwords to be proud about.