So if I kill Commander Niall I can go directly to the Snowfield skip without getting the Haligtree Secret Medallion (Right) at Albinauric Village?

I know in the rules it says "Snowfield skip is allowed, including deathcam, but only after you have defeated Niall in Castle Sol, since the boss is a requirement to get part of the Haligtree medallion. Keep in mind that only defeating the boss is required, but you don't have to pick up the medallion." but just want to make sure

Well, I believe the mods would have to discuss it. I don't often watch speedruns myself, so I can't say for sure, but there's at least two points that can lead to different interpretations.

1 - You see, the phrasing does seem to imply that you're entirely correct, and you don't need to march to Albus. That would apply to All Remembrances (DLC included) too. 2 - ... however, "SINCE the boss is a requirement to etc." seems to imply you need to fulfill all the requirements to be able to get the medallion piece, even if you don't need to pick it up. What would be considered a requirement to get Albus's piece is unclear. There are no bosses, it can literally be the first thing you pick up in the game. So, talking to Albus? Dispel his illusion? Just sit in the village's bonfire? One would think something needst be done, but it could also just be that only bosses are considered barriers for acquirement of key items, and so making key items unecessary if there are no bosses that would normally lock them, should you find a way around via a non-glitch skip.

Yes, you dont need to acquire medallion pieces if you do the skip. Just have to kill Niall beforehand.