Everydaygame, I did look at that image you attached more carefully, and I do think I see where the confusion is.
If you look at the axis of the graph you will see that they are indeed using the opposite sign convention scheme as 2H+
appears at 0.0V and 2 H2
(g) + 4 H+
+ 4 e−
appears at a value on the graph of positive ~+1.2 V. The problem here if you notice is that the *entire y-axis* on the graph has been inverted as values of -.05 and -1.0V are going up whereas positive quantities such as 2.0V and 3.0V are going down. So if we look at the image on the right and expect -1.23V because one half reaction appears "lower" than the other, we might suspect they made an error but actually what they did is flip the entire y-axis upside down from what we are used to.
They aren't incorrect to do it this way. Because the numerical value remains the same (as Borek and Bee have mentioned) either way you go, we can easily just revert the y-axis back to it's normal orientation if we want by switching the positive and negatives on the y-axis while leaving everything else in the image the same. Then the gap between the half reactions becomes -1.23V like you might want. But since the y-axis is inverted on the image, then the value of 1.23V is correct.
Why did they invert the y-axis on the graph? I don't know, but at least from the y-axis flip you can conclude that they did know what they were doing and probably had some compelling reason to do it this way (perhaps to fall in line with sign conventions? Notice that the x-axis is also backwards from the way we do things typically).