Everything written in their TOS and other pages about the rules matters. It's clearly written there and you are obliged to provide them more information, including your ownership of the content if they need it.
Code:
You may Post only User Content which you own, have created
or which you have clear permission to Post.
The above is not a simple statement as it sounds! (There could be more statements like it specifically addressing your case which I may not be aware of). Find the above statement on their site. It clearly means that if they suspect you have not created the content, or don't have clear permission to post, then they can remove it and ask for more information.
They can even ban you if you haven't given them an understanding that the content (you got written from another person) is not wholly created by you.
You still have / don't have sufficient legal paperwork to display the full ownership of the content.
If you don't have the complete ownership, it's putting them in a soup with the original writer, who incidentally hasn't 'signed' their contract. This can be a long legal process with the original writer who can demand full compensation for 'stealing' his original work. The court will need sufficient paperwork to prove that they indeed have the authority from the original writer, and not someone who has stolen content / hired another person to write on his behalf / or whatever. The company only wants to deal with the original writer for many such issues.
So, if they get a "written" complaint / proof from some "writer" who shows that, for example, even though you've gotten the content from that writer BUT without the written consent of the full transfer of ownership, then they have every right to believe the "original writer", do the necessary investigation, and can ban you straight away for at least a breech of contract or whatever.
They of course don't have the obligation to tell you every reason behind the rejection. They have given you an explanation which they can defend any time successfully with "proofs".
Can you really prove the full ownership of the content if they ask for it? For example, in this particular case, the content is still unpublished, right? So how can anyone else show them the same content (or a very similar content) and also give them the name of who is going to publish it? If they get this type of proof, then find that you have already submitted the content written by a third party and haven't provided that information with the proof of your ownership, you are in deep trouble and also have put them in future trouble unnecessarily.
I'm not a lawyer, but I understand these things lot better. I also have over 2 decades of experience in the field of computers and have seen such things happen to lot of large companies. Why do you think they have a billion-words TOS and still have other pages of rules, special conditions, and whatnots? To simply save their hide when they get into trouble for any reason. Take a great advice in this matter from a real lawyer though.