You could argue, Oda does it on purpose. He wants the ambiguity.
If Brannew said that, it implies He knows Mihawk's Secret, which doesn't make sense,
All They know is that what Mihawk can unleash with his Sword is Superior to what Shanks can,
Mihawk's First Words were literally about how a Sword by itself is "Nothing",
Your Swordsmanship is based on what you actually use to Fuel it,
We've seen Strength, Speed, CoA, CoC, Soul, Room, Gravity, Fire, Lightning, Underworld, Ice, Shockwaves, Poison, Rokushiki ... etc
Zoro literally grabbed a Pillar with his Sword & called it Three-Sword Style whatever,
So Mihawk's Swordsmanship = What "Fuels" his Sword? (Beside Strength, Speed, Haki ... etc)
No one knows so far, including us Readers, and same for Marines/WG,
For example, People don't know Haki, which means it's not mentioned in Newspaper, which means People don't know Shanks Power, however, They do know about DFs & read about their Users in Newspapers,
Even someone like Wano Luffy wasn't aware that you can coat CoC for example, so imagine knowing what is Mihawk's Power?
Probably no one does, except maybe one or two people, so from everyone's perspective, Mihawk is the guy who uses a Sword to better results, nothing more.