On September 29th, 2016, Speedrunners were able to beat Super Mario 64 with only a single key thanks to the discovery of Parallel Universes.
https://www.youtube.com/watch?v=j5j6l9ULxmI
Grayda was correct in theorizing that the first Bowser fight could be skipped using the "Parallel Universes" (PU) glitch described in his question.
If the name Parallel Universes makes it sound like this glitch is horribly complicated and difficult to understand.... that's because it is.
If you want an in-depth explanation of how Parallel Universes work in Super Mario 64, I recommend watching Watch for Rolling Rocks - 0.5x A Presses by pannenkoek2012. (Explanation of PU Glitch begins at 10:32)
If you don't have time or patience to watch someone talk about Parallel Universes for 15 minutes, I'll try to summarize the trick as best I can.
(Summarized from Speedrun Description on TASVideos.org)
In Super Mario 64, there is an underwater moat door that can be used to access the basement. If the basement door could be opened while it was still underwater, it would make the Basement Key earned from the first Bowser Fight completely unnecessary.
By hacking the game, the SM64 community discovered that the moat door was fully functional underwater, and that there was a 1 frame window where Mario could run underwater and open it.
Tyler Kehne is definitely not sonicpacker.