I think two of my sentences are the ones that are causing the confusion. When taken in the context I was explaining, I think they make perfect sense but I accept that I might not have explained it well to someone else. I'll try to explain them better below.
In a climbing turn, the outside wing has a higher angle of attack which translates to a higher stall speed.
This quote is talking about why, in a climbing turn, the outside wing stalls first. If you look at the link I included, it shows that in a climbing turn, the outside wing is at a higher angle of attack. Assuming that both wings will stall at the same angle of attack, if I now slow down in this condition (outer wing having a higher angle of attack), the outer wing will stall first as it will reach the critical angle of attack first - assuming that I don't change anything else. This is what I meant when I said the outer wing will have a higher stalling speed in this case.
I need to increase lift to stay in a level turn so instead of increasing speed, I increase angle of attack and that in turn will increase my stall speed.
I think we all agree that in a level turn you need to increase the lift, which causes an increase in load factor (and an increase in stall speed) to maintain your altitude. So now in the banked condition, I need to find a way to increase the lift.
Lift = 0.5 rho Vsquared S Cl
I can simplify it since I'll assume that the density stays the same and that the surface area of the wing doesn't change. It then becomes:
Lift = Vsquared Cl
To increase lift I need to either increase the speed or increase the Cl or a combination thereof. Cl essentially translates to AoA. So I either increase my AoA or I increase my speed to get the extra lift. Assuming I do not want to increase my speed (like I stated in the quote), I need to increase my AoA. Increasing my AoA in this situation puts the aircraft into a load factor higher than 1. Since the stall speed is directly related to load factor, I have now increased the stall speed in this scenario. I think the confusion came from me not summarizing that this increase in AoA, increases the load factor (because I'm maintaining the same speed which results in more lift than weight now) and, therefore, increases the stall speed.
I was only talking about the airplane in a turned condition with no increase in speed. In that case, I believe it's perfectly correct to say that the stall speed increase is due directly to the AoA increase - that is the root cause in this case. In a 1G condition - ie: slowing down in level flight - this is not the case as the 1G condition dictates the stall speed will remain the same.
If it's still not clear, let me know.
Other than that, I think we're all in agreement.