The language in the document has no effect on his position with the show. The document has no effect on his job or actual title with the show or the company.
The word "Producer" was simply picked as a word to be used in place of the company name within this document. Any time you see "Producer" in that document (and no where else), simply read it as saying "Sixth Avenue Production, Inc." That's it. It really is just a common method to avoid repeating the same, long name of some business in drafting these documents.
For example, "NoZed Avenger Prime Bottling Co." may be one party in a contract. Under the law, you would want to use the full name of the company to make sure that the rights and duties in the contract all apply to the right company. But writing "NoZed Avenger Prime Bottling Co." every time that you want to say "NoZed Avenger Prime Bottling Co." or refer to "NoZed Avenger Prime Bottling Co." is unwieldy -- see how hard it gets to actually read the terms?
So, at the first of the document, I would state that "NoZed Avenger Prime Bottling Co. is hereafter referred to as "Distributor" within the agreement. Now, all I have to do is type that Distributor agrees to provide x and Distributor promises delivery on y date. Much easier to read.
I, NoZed Avenger (personally), may have the title of distributor with the company -- but it is clear that "Distributor" in the agreement refers only to the company with regard to the rights and duties set out in the document itself. If "Distributor" in the document promises to deliver product by the first of the month, it is the company that can be sued for that failure -- not me personally. And, though I may have ten "distributors" working for me, none of them is personally resonsible for the delivery -- it is only the company as a whole ("Distributor" as defined by the contract) that can be sued directly.
In the same way, the person in the JE document agrees that "Producer" (read as: Sixth Avenue Productions, Inc.) is not responsible for the statements from JE, but JE will be. He is still a producer of the show.
The choice of the word "Producer" does not affect the "real world" definitions of what JE does for the show. It is perhaps unfortunate that they chose the word "Producer" to refer to the company, instead of "Company" or something similar.
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