This is a fairly apt summary.
It probably sounds like a weird thing to get hung up on, and I'm not usually a stickler for details like this-- after all, the end result is always going to be "fighters chosen by Nintendo and approved by Sakurai." But I think the narrative of "he was given this potentially huge list of characters and is just picking the ones he wants" could be greatly overestimating the amount of creative freedom he has. Using his perceived biases when appraising a character's chances seems like a mistake.
I think even with the most accurate translation imaginable, even to a native Japanese speaker, there's no way to get the "truth" out of Sakurai's statement. I sort of jokingly suggested that, while Sora Ltd. isn't owned by Nintendo (at least not as far as I know), and therefore Sakurai isn't really a Nintendo employee, he works for Nintendo since they own and publish Super Smash Bros., and as a result, his own choices technically qualify as Nintendo's choices. Would he tell a half-truth like that? Who knows.
Given that the translation also states that he "can still say no", I wouldn't actually count out his creative freedom. To our knowledge there's only one character that his hand was ever forced on, and that's Corrin - hell, that might not even be our "knowledge" but some fan rumor that started flying around because of how absolutely sick of Fire Emblem characters most Smash players are, and having one past Roy that's a walking advertisement rubbed everyone the wrong way. How does anyone prove that Sakurai said no to a character because he would prefer another one? Isaac and Zero are doomed to an assist trophy while Piranha Plant and Isabelle are playable characters, there's no rhyme or reason to why he would think a character wouldn't "work". Even characters he outright said wouldn't "work" like Ridley, Villager, and Miis are in the game as playable fighters, his selection process is probably a mystery even to Nintendo. Abstract as it is, he might even consider how popular a character would be with the fans to be something that does or does not "work".
I think the "how" is the mystery of Smash development. Whether there's a focus group or a laundry list or Sakurai just takes emails from random Nintendo employees and considers it, that's what would really put people's mind at ease (or drive them up the wall) to know. There's a massive inconsistency with the common perception of "Nintendo chose the fighter lineup" and Joker, Banjo, and Terry, and that's if we consider Hero the true shill character.
My best and truest guess actually is focus group. "Nintendo chose the fighter lineup" doesn't even say DLC, we're the ones who put that word into Sakurai's mouth this time. If we take it at face value, Nintendo chose:
Everyone is here
Inkling, Ridley, Simon, K. Rool, Isabelle, and Incineroar (along with echoes)
Joker, Hero, Banjo, Terry, Fighter 5
The future
In which case Nintendo chose nothing but popularly requested characters, Incineroar, and then off the wall picks, much like Reggie said "fighters that you would never expect to be in Smash Bros" for the Fighters Pass. They didn't shill a damn thing, they gave us exactly what we wanted and likely will continue to do so.
And for what it's worth, after Brawl and Smash 4, Geno
IS a character I would never expect to be in Smash Bros.