In order to fully grasp what this is about, it is important to get some context on Haydn White. White is a historian with a strong relation to literary criticisms. In his book Metahistory: The Historical Imagination in Nineteenth-Century Europe he writes that the writing of history is very similar to the writing of literature, whether in a primary source or in studying history in that they both attempt to tell a story; a story which has a plot. Basically, the idea is that whenever we write a book about history (leaving primary sources aside for now), we attempt to tell a story that follows a basic plot. When writing history, we pick a starting point and then an end point and in between these two points a plot unfolds. We tell the story of a historical development, which like literature tells the plot of something happening. This is the historical narrative we chose.

For example: Say, we want to explain the French Revolution. In order to that, we can start with the year 1789 and the meeting of the estates general and then go on to tell the story of what the historical figures we know to be of historical significance like Robbespierre, Danton etc. went on to do until Napoleon takes over. Or we can start with the ideas of Kant and other Enlightenment philosophers and see how they influenced the actual policy that transpired without going into details of the actors involved. Or we can tell the story of how the Revolution affected a Parisian cobbler. Or we can tell a story that doesn't focus on France that much but rather on Haiti, where the Revolution sparked another revolution. We also needn't stop with Napoleon but can include him as a product of the Revolution. Or we can stretch out the history of the French Revolution to encompass the whole century up to today because its influence still ripples through time by establishing in practice so many of the things we tend to see as the basis of a lot of our political systems today.

All these attempts to explain the French Revolution and its significance rely on the same set of basic historical facts but tell different stories. And prima facie and also on a second look, all these narratives are valid but framed differently - following a different plot. This was on the one hand important for it was crucial in establishing that language isn't a neutral medium to transfer truth but that the way we narrate history is by itself part of the interpretation of history. White, however, took this theory even further and asserted that, fundamentally, there is no difference between writing history and writing fiction and that historical events are always somewhat contingent on how they are emplotted and narrated by society and historians. For White, the category "The French Revolution" is an emplotment device for a collection of things that occurred in the past and are related to each other by both contemporary and later actors imbuing them with meaning through a structure of narration.

So when White talks about the Holocaust, he isn't referring to the fact that millions of Jews were killed by the Nazis, he is referring to the historical narrative and plot that has been established in historiography and public consciousness around it. In 1992 he wrote the article Historical Emplotment and the Problem of Truth in Saul Friedländer's Volume Probing the Limits of Representation. Nazism and the “Final Solution” in which he addresses his position on the issue.

Pointing to such representations of the Holocaust like Art Speigelmann's comic Maus and Andreas Hilgruber's controversial book Two sorts of ruin, the point White is trying to make is that as a set of historical facts and events, the Holocaust does not mandate certain narratives and emplotements while making others impossible. Maus as what he refers to ironic emplotment represents a much more impactful work on the subject than Hilgruber's book e.g.

As White wrote in a paper about Friedländer's books on the history of Nazi Germany and the Jews:

How to represent the history of an event which destroyed a wide variety of kinds of Jewish communities as well as other kinds of communities, races, groups more or less unconnected with one another in space, time, and culture and in different kinds of relationships with the host countries in which they had come to reside, and their reactions and responses to a machine designed primarily for the purpose of exterminating them?

only to later conclude:

A photograph of a historical event is a good illustration of this principle because its substitution by a description shows how any historian’s gesture toward a real referent in the past must already presuppose a description of that referent to serve as the referent’s discursive stand-in. This does not make the events being described less real or more fictional. It is simply that the description of any historical phenomenon is a way of constituting it as a possible object of historiographical representation.

What this all boils down to is not that White is saying one cannot prove that the Nazis killed millions of Jews and others during their reign and during the war, just that past events do not impose on us ways to write about them, to narrate them, and to emplot them. Rather, a wide variety of emplotments and narrations is possible.

Now, this might all be fine and dandy for White who tends to approach history as literature per se and while his contributions in terms of actualizing the narrative as something for the historian to keep in mind, his very unconditional reading of narrations and emplotments is all going a bit overboard.

We know of course that we as historians will be guided in selecting materials for the stories we tell, and in the way we put these materials together and interpret them, by literary models, by social science theories, by moral and political beliefs, by an aesthetic sense, even by our own unconscious assumptions and desires. It is an illusion to believe otherwise. Yet, at the same time, history still is an empirical undertaking and while many choices are involved in how to present and write history, the sources available and the actual facts of the past still do their part in imposing certain structures of narration onto us. When writing a history of Nazi mass killing, we can absolutely start in 1921 or 1933 in order to trace ideological factors but it is still a fact that the first Nazi mass killing programs started in 1939 and not 1935, simple as that.

In this sense, history does impose certain restrictions in terms of narrative and structure onto us, simply because as an empirical undertaking we have the responsibility to be truthful to our source and we can't make stuff up because it makes for a better story and more dramatic plot.

So, yes and no. Hayden White is, of course, controversial in the field of history. His assertions tend to spark debate. I believe this debate occurred during the early 90's, a time when studying the Holocaust was coming into the mainstream (for reference, the Holocaust Memorial Museum in DC opened in 1993) and around the time Deborah Lipstadt published her book about Holocaust Denial (which was the subject of David Irving's libel case). So yes, his claim that we shouldn't be considering a "proper" reconstruction of the Holocaust was controversial. But I haven't seen a ton of debate specifically tied to the UCLA one.

Some book reviews for his "The Practical Past" (in which he uses the Holocaust as an example of his theory of tropes) have come out, but so far they seem to be more concerned with discussing his ideas than debating his theories of the Holocaust. I will say that White is well known in history, he was part of the linguistic turn of the 70's and Post-Modernism in the US, but this debate is likely not well known.