Ok. The definitions I see are "point-by-point" not "line-by-line." But it's not really worth debating that here anyway. My fault.
Sure it does. If your group has determined that 10 different means are acceptable. Then which one of those 10 you use doesn't matter.
Actually, one of the reasons I love D&D is that it can provide a safe place to explore complex psychological and morality questions with a group of friends. Nor did I say you could "do anything" do achieve it.
So, considering this and other answers, I think I've come to a potential definition of Illusionism.
Illusionism is the illusion of a choice.
The classic example is along these lines: The DM has prepared an encounter. We'll say it's an ogre.
The characters have a choice - could be a fork in the road, but we'll say the forest or the swamp.
Regardless of the choice made, the players encounter the ogre.
Scenario #1
1) The players are given a choice.
2) The results aren't fixed until the choice is made. The DM doesn't place the prepared encounter until after the choice is made.
What about a random result? It's the same fundamental thing:
Scenario #2
1) The players are given a choice.
2) The results aren't fixed until the choice is made. The DM determines the results randomly after the choice is made.
What about when the result isn't prepared ahead of time?
Scenario #3
1) The players are given a choice.
2) The results aren't fixed until the choice is made. The DM determines the results on the fly after the choice is made.
So what's different about them?
Well, in scenario #1 there is no choice. There's only one result.
In scenario #2 there also is no choice. There are multiple possible encounters, but still only one actual result (roll on the random table).
In scenario #3 there is also no choice. The result can be be authored to relate to the choice. But there is still no choice.
It's really just the method of producing the result that differs. Otherwise they are identical, at the point of making the choice, there is no choice.
Now a term that has come up a number of times is "meaningful choice." For the choice to be meaningful, they need to have information ahead of time, and the information has to relate to the results. That is, it helps them make a choice.
In scenario #1, the DM could provide clues as to what lies ahead, and they could be different for the forest and swamp, and yet still relate to the prepared encounter. In addition, the characters could later go down the other path, and the DM could provide a solution then that still relates to the information given. In which case there are now two meaningful choices.
In scenario #2, there could be two tables of random results, and the information provided could differentiate between the two. So a meaningful choice could be made - table #1 or table #2. But this is no longer scenario #2, because now there is actually a choice (table #1 or table #2)
In scenario #3, the DM can base the results off of the information provided to the players. Then when the choice is made, the result authored will be meaningful. But it's still the same state of scenario #1 - there is no other result until the DM authors one.
Other than scenario #2, there is still no meaningful choice. The results may be meaningful, but that's different than a meaningful choice.
It seems to me that the idea of Illusionism lacking a meaningful choice is a bit of a red herring. It sounds like it should matter in the definition of Illusionism, but it doesn't actually change the underlying mechanism. Either there is a choice or there isn't. And Illusionism being the illusion that there is a choice.
For example, you have two actual choices. Down road #1 is an ogre, and down road #2 is a dragon. Whether you have any information to help you make that decision, or the information you have is false because somebody is trying to get you killed and wants you to meet the dragon, it's not Illusionism. Because you have an actual choice.
Note that there are situations where there is no viable choice. But that's not illusionism. You captured by a tribe of orcs, and you have the choice of being sacrificed to their volcano god (thrown in the volcano) or dragon god (being fed to a dragon). There isn't a good choice, but it's not Illusionism. There is a choice, and it's clear that there is a choice. You just don't like either of the results.
Scenario #3 makes it easy to make it seem like the choice was meaningful. In fact, the GM is usually instructed, or even bound by rules, to ensure that the result directly relates to the information available and the choice that was made. But it's essentially a more sophisticated application of Illusionism. The illusion being that there is actually a choice. Because the DM could provide a result that doesn't relate to the information or the choice. The DM is in full control of the result because the result hasn't been fixed before the choice has been made. The rules may instruct the DM to provide a solution that relates to the information and/or the choice. But that's different than an actual choice. It's really just instructing the DM to ensure that the result makes it appear that they made a meaningful choice.
The only way to avoid Illusionism is to ensure that any choices provided have at least two actual results. Which means the results need to be pre-determined, even if it's only moments before the choice during the course of play that the DM comes up with the potential results.
To go back to the original post, what about railroading? Is Illusionism railroading?
Well, in all three cases the DM is still in control of where the action goes. That is, they have control of the story when providing the results. With both scenario #1 and #2, the DM can prepare results that are acceptable to them and the adventure at hand. Thus they can be used to keep the adventure "on track." But they can do the same thing in scenario #3, in that the only results they provide on the fly also keep the adventure on track.
The advantage of Illusionism, when used with skill, is that it's more subtle, potentially undetectable, compared to a more overt approach, such as, "no, you can't go there." A "you can't go there" approach can be dungeon walls, a cave-in, an enemy force too great to defeat, or any number of other options that place a boundary on where the adventure can go.
On the other hand, it's easy to avoid, there just needs to be an actual choice - at least two different results - before the choice is made.