If enough inputs are available online, someone can presumably collect them and clone the entire project without having access to the puzzle input generation code, which is the "secret sauce" of the project.
He's also described, over the years, his process of making the inputs. Related to your comment, he tries to make sure that there are no features of some inputs that make the problem especially hard or easy compared to the other inputs. Look at some of the math ones, a few tricks work most of the time (but not every time). Let's say after some processing you get three numbers and the solution is their LCM, that will probably be true of every input, not just coincidental, even if it's not an inherent property of the problem itself.
There has been the odd puzzle where some inputs have allowed simpler solutions than others, but those have stood out.
if we just look at the last three puzzles: day 23 last year, for example, admitted the greedy solution but only for some inputs. greedy clearly shouldn't work (shuffling the vertices in a file that admits it causes it to fail).
I have a solve group that calls it "Advent of Input Roulette" because (back when there was a global leaderboard) you can definitely get a better expected score by just assuming your input is weak in structural ways.
But there are enough possible inputs that most people shouldn't come across anyone else with exactly the same input.
Part of the reason why AoC is so time consuming for Eric is that not only does he design the puzzles, he also generates the inputs programmatically, which he then feeds through his own solver(s) to ensure correctness. There is a team of beta testers that work for months ahead of the contest to ensure things go smoothly.
(The adventofcode subreddit has a lot more info on this.)