I would think that you would approach this from several angles.
As can see from their three graphs, the conditions that they use to generate are very controlled and they 'somewhat' define them, that is, that used a different part soldered to a different printed circuit board (PCB) with various dimensions. Have you duplicated these conditions for your readings including times, the PCB, the voltages, etc.?
These curves are 'typical' responses under those very controlled conditions and your mileage may vary because there are many factors in play.
If you look at aL35 Spec Sheet, you see that these are called 'typical' charts and there can be a pretty wide variability as allowed by the specifications of the part.
Additionally, in that spec sheet, you see that they 'guarantee' 'Accuracy versus Temperature' and I would recommend trying to validate that the part is meeting those criteria as the typical graphs may be difficult to recreate since there are so many variables.
I would also suggest asking the part manufacturer for more details of the hardware, circuits, PCBs, et. al. in order to duplicate those results. Maybe even the Application Engineers, but I doubt you would make much headway.
However, validating the 'Guaranteed' performance numbers and playing with those characteristics in order to massage your measurements will likely be the most fruitful approach.