The claim is likely true to what the DNC argued but the plaintiff used the term "enforceable obligation" in a summary. The defendant, the DNC, having never said that used only terms "contractual and fiduciary obligation" and "enforceable promise."

You can see the quote in full from the transcript here

MR. BECK: Yes. And I'll take the last part first, which was the question your Honor had posed, is there -- and I'm paraphrasing it, but is there a material difference between a campaign promise, such as "read my lips, no new taxes," and representations that are made in the DNC's own charter? And, quite frankly, if what defendant -- or what the DNC has just said is true -- and I really hope it's not true, but if what he said is true, then I think it's a really sad day for democracy in this country. Because what essentially the DNC has now stated in a court of law is that it believes that there is no enforceable obligation to run the primary elections of this country's democracy in a fair and impartial manner. And if that's the case -- and I think counsel just said it himself -- then really, you know, the sky's the limit in terms of what the DNC and any party, for that matter, can do.

The key here is that Jared H. Beck is the attorney for the plaintiff. Not the defendant (the Democratic National Committee).

Now what Beck is responding to is a series of claims argued by the defendant, Spiva, acting for the defendant, did say

"we could have [...] voluntarily decided that, Look, we're gonna go into back rooms like they used to and smoke cigars and pick the candidate that way. That's not the way it was done. But they could have. And that would have also been their right, and it would drag the Court well into party politics, internal party politics to answer those questions." "the party has the freedom of association to decide how it's gonna select its representatives to the convention and to the state party." "there's no right to not have your candidate disadvantaged or have another candidate advantaged. There's no contractual obligation here. Nor is there a fiduciary obligation, although I know we're gonna get to that later. But there's -- it's not a situation where a promise has been made that is an enforceable promise."

Given the context about it being the freedom of association for a political party to pick a candidate in a cigar filled back room after a primary that had one candidate disadvantaged and having said explicitly both "contractual obligation" and "fiduciary obligation" it may not be much of a stretch for Beck to have summarized that the DNC was arguing that there was no "enforceable obligation"; and, the DNC did say explicitly there was no "enforceable promise."

Update

As to whether or not the DNC claimed the primary was fair, they did claim such but they expressly stated that such a claim was not their argument, in fact they argued that to even entertain that question would invalidate the First Amendment interests of the party.