I'd say there are also two different facets to backstories that we should consider. There's the backstories that inform who the character currently is... theoretically giving the player inspiration for how they choose to play the character, and little nuggets of information they can drop in as they play the character (like vocal quirks, fears, things that trigger various emotions etc.) These things just help the player roleplay and inspire the player with who the character is meant to be. They don't really impact the DM at all.
The second type of backstory of course though is the one that is pushing the character forward and has not yet been fulfilled. The character has unanswered questions they need answered, or important events that have not yet finished, or people they have conflict with that haven't been resolved. These are the ones that I imagine would be considered the potential "railroading" scenarios the video talks about (please note I haven't watch the video yet.) These are background stories that are meant to pop up during play and be interacted with, potentially being solved, but not always. So in that regard, the "railroading" aspect is the players are putting stories in front of the DM and expecting the DM to move the game in such a way so as to have these scenarios and events come up (and thus allowing the players to interact with and/or resolve them.) And depending on the number of these potential stories... you might have a game that has so many backstories to deal with, it might seem like the DM has no ability to present their own.
I will say though that I myself actually like that as a DM. It fits my personal style really well. Because I am not a DM who creates his own stories... I'm very much a DM that takes published adventures and modules and then runs them through various blenders to fill out an adventure / area / world for the players to play and for me to improvise around. So for me... these backstories are just more material that gets thrown into the blender. And as we are hitting story blocks A, B, & C... there might be a call in some module that I'm using for a particular person, and I realize that the person from the module could easily be replaced by X person from a player's backstory. And now suddenly that player has a more personal connection to what is going on because their histories and being brought to the fore. I find these moments when I can drop in bits and pieces of who these PCs are into the narrative to be fulfilling for me, and hopefully fulfilling for them too.
I will say though that D&D as a game does not go out of its way to assist you in running this type of backstory driven gaming. For that kind of thing... my go-to is always 7th Sea (especially 1st edition). In that game-- a game built and designed as a romantic swashbuckling adventure type of experience-- the players would specifically BUY background events during character creation in order to have those events show up during play and help influence the story of the game. They are specifically chosen to emphasize the theme-- a Vow a PC has taken, a Lost Love the character is trying to win back, a Nemesis that destroyed their family and for whom the character is seeking revenge-- and have these backgrounds crop up during the adventures. And when they do so, they give the players additional XP as part of the session. And quite frankly... you oftentimes get MORE XP for the session from your background events popping up and driving a session's narrative than you do for just the normal XP given every session for playing. That is a game whose focus is to marry a character's trials and tribulations into the narrative, and for whom the DM definitely has to keep one eye looking forward, while also keeping one eye looking back on all the backstories the PCs have in order to incorporate them.
And like with anything... some GMs probably love it, and some find them to be a hindrance or a "railroad". But that's true with anything having to do with any RPG.