According to lawsuit, Subway’s tuna sandwiches contain “no scintilla of tuna”
thecut.com
thecut.com
That's an unusually strong statement for them to make if it's untrue, there's not much wiggle-room there.
That or they are complaining that a tuna sandwich doesn't have the advertised ingredient.
(Edit: Saw that albacore is now "near threatened")
Sadly, I can't find the "one third" claims any more, closest I can find right now are several "less then 50%" articles with addenda from around 2017[1][2][3].
[1] https://arstechnica.com/science/2017/02/whats-in-subways-chi...
[2] https://www.cbc.ca/news/business/marketplace-chicken-fast-fo...
[3] https://www.npr.org/sections/thetwo-way/2017/03/01/517920680...