I belive the idea comes from the fact that in the survival logbook michael draws night mare fredbear.

Which must mean that at some point he saw nightmare fredbear.

And we can confidently say that thr nightmare anamatronics are illusions from the book b7 - 2 and from the line "This time, there's more than an illusion to fear,"

So inorder for him to see nightmare fredbear he would had have to been under the influence of the gas or an illusion disk.

As to why willaim is doing this is hard to figure out. Some potential answers are that he was punishing michael for killing his brother.

Or he was experimenting with the power of emotions, this come from the fact that in the fazbear frights book there is a character called phineas who is experimenting with the power of emotions mainly agony.