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Related: How much weight should we give authors' declarations of their intent after the fact?

Just to give a concrete example of what I'm asking about, I'm thinking in particular about The Hunger Games books and movies. Since the book was written entirely from the perspective of Katniss, the movie has a significant amount of detail that the books didn't. For example, in the movies President Snowe explains why they have the Hunger Games in the first place instead of, for example, just rounding up kids at random and executing them on the spot.

Suzanne Collins is, at a minimum, listed as one of the first movie's screenwriters (although she's not listed as a screenwriter for all of them, such as Mockingjay part 1). She was presumably still involved in the creation of all of the movies, though.

That being said, assuming that authorial intent has some bearing on how we interpret the text, is it "valid" for us to use the additional information introduced in the movies to interpret the books?

Regarding authorial intent after the fact, a number of complaints from readers boil down to "If the author wanted to include that bit, it should have been included in the books to begin with." These are stricter textualists, who proclaim that canon is only what's on the pages of the novels, period. So they object to the idea that JK Rowling can say that 20 years ago she intended for Dumbledore to be gay, and Nagini to be a woman under a curse, when that was not spelled out in the original seven books.

If a third party makes a movie or series of movies about a text or texts (Peter Jackson with Tolkien, the Marvel Cinematic Universe vs. the comics), readers can argue that they are from different authors, and therefore "movie canon" is not "textual canon."

However, what you're posing is that the writer/creator of the text is additionally a writer/creator of the film.

I think in that instance, it's valid to consider that the writer is "including that bit" which didn't make it onto the pages. In the specific case of The Hunger Games, Collins chose to stay in first person and did not allow Katniss to overhear anything Snow might have said about the origins of the Games. The films did allow that perspective, so she now has the opportunity to canonize those ideas. Similarly, since Rowling wrote the screenplays of Fantastic Beasts, whatever she is writing and creating can be considered part of the same universe.

But: "valid" does not equal "obligatory." As a reader/audience member, you are free to declare that for yourself, film canon and textual canon are not congruent.
Many Potter fans consider The Cursed Child to be Rowling's fanfic of her own universe because certain aspects of it seem so out of character and contradictory of book canon. You can ignore the prequel trilogy of Star Wars because of quality problems, but accept Rebels as canon. Certain Trekkies cheerfully ignore Star Trek V, VOY's episode "Threshold," or the entire Abramsverse.

If you want to use the films to contribute to your interpretation of the books, I think you have a solid argument because they are written by the same person. But they are not on the same unequivocable footing as Book 4 of 7.

When trying to determine authorial intent, it is reasonable to use any source from that author, as long as it is not contradicted by a more direct source. The only problem with using movies in which the author had input is that you don't know how much is from the author and not others, and how much of it was changed for the sake of the adaptation, e.g., to look good on screen.

As such, simply showing information from the movie can be used to argue authorial intent, but cannot prove it by itself.

For example, in the case given in the Question, you have a rather significant detail that fills in important information about the plot in the book and movie. There isn't much reason that the explanation would be different in the book than in the movie. You state the author was rather involved in the making of the movie in question. And the author has not made any contradictory statements.

You can thus make a reasonable assertion that this scene most likely represents the author's intent. Not simply because it is in the movie, but because of those other factors.

On the other hand, if you wanted to assert the exact physical form a spell from Harry Potter took, you would be on far shakier ground. Such a detail is rather insignificant. And it would be very possible that something was made to look different on screen. It is reasonable that the author did not concern themselves with this. (Plus spells looked different in different movies.)

Despite the author's heavy involvement in these adaptations, it would not be reasonable to infer authorial intent from the way a spell was depicted. You would need further evidence.

It is generally a bad idea to assume that the movie is the same as the book. Even when the author is a stickler for control, and manages to get his or her own way, things must be adapted for the screen. Frequently characters are omitted or sidestepped.

My favorite example is Ayn Rand's 'The Fountainhead,' where she was both author and screenwriter. She tried for tight control, but still had to omit some of her lengthy novel's scenes and characters. Here's a good article that contrasts her experiences (including the issues of censorship and ad-hoc rewriting) against the usual situation for screenwriters. http://productioncode.dhwritings.com/AR/AR4.html

Occasionally the movie appears first, and a novelization, perhaps ghost-written, appears later.