The attempt on a later POTUS that also left Brady in a terrible condition was carried out by a guy with a mental problem. I believe at that time there was a lot of digging to see if he was connected to any 'political' or 'social' group that may have made that a high mark on their agenda. Nothing came up. He just watched too many movies or a rerun of one movie and maybe that's what drove him nuts. Seeing that movie more than once would drive me nuts too. I guess they figured he wouldn't be a problem to any future POTUS so they let him come home on weekends to see his parents. He was just crazy. Nothing deeper.
I remember in our history classes we always were aware that John Wilkes Booth killed Lincoln. It was waaaay later that I learned there was a lot more to that story and there were others involved too. I guess they just didn't want to tell kids that a woman was hanged because of the whole thing. We were in the Ozzie and Harriet days and the only bad news we heard was when Eddie rang the Cleavers doorbell. Then the Civil Rights movement cranked up to full blast and we were bombarded with info we didn't quite understand how to sort out. All of a sudden Lincoln's assasination was brought back out of the file cabinet and the rest of the story was told. So, for the next 20 or more years, we heard the 'South' was the root of ALL evil. Understanding how that worked, and it still is in some respects, it stands to reason the South was blamed for the actions of one man. The one who pulled the trigger and hit Lincoln in the head with a bullet. The other unsuccessful attempts that night were footnotes in the story for 100 years. They still take a back seat except on the History Channel where they like to replay the thing about every six months.
So, I think that Wirtz was given a bum rap and used as a stand in for the other leaders of the Confederate cause and Dr Mudd was given a bum rap too. He was just a Doctor. The others who were hanged are spoken of like I said, on the History Channel. I still haven't seen em in the textbooks. But the South is still held suspect to this day though there's no evidence to show anyone connected to the Confederate cause had anything to do with it.