To answer this properly, one first has to understand how your FMS, FMC, or GPS calculates distance and track between fixes. While these will normally line up within a degree or two between the unit and the chart, there are some units where the difference can be as great as 3 or 4 degrees.
The reason for this is that many FMS/FMC units calculate their tracks in degrees true and use a standard variation model for a large geographic area to present magnetic information to pilots. In slightly more technical terms, it is the calculated true track between two locations that is passed through the Kalman Filter, out of which the true heading is obtained. The FMS then applies the variation adjustment to this true heading to display to the pilots.
For example, the variation in Calgary, Alberta, Canada is presently 14.14 degrees. However, the FMS that I use seems to sit in a geographical area programmed for 16 degrees. This automatically puts all approaches into Calgary at near 2 degrees magnetic off from the charted publications.
So, is this an issue? No, because the FMS manufacturer has stated that approaches may be up to 4 degrees from the charts due to the use of the variation model. Any greater, and then the underlying true track that is actually used to navigate should be considered suspect.
So, when someone says:
the maximum allowed discrepancy between the chart and the box is 1 degree for LNAV and 0.1 for VNAV
they are likely referring to an FMS/FMC type that utilizes a higher-quality variation database, or a unit that is programmed to calculate magnetic tracks, not true tracks.
How does this all relate to your question?
Well, discrepancies are going to exist between the chart and the unit you are using. As you are not allowed to modify any procedure retrieved from a box you have to know whether the discrepancy you see is within the tolerances from the unit manufacturer.
If the difference you see is within tolerances, then you can consider the unit and the chart to match and you may fly the approach.
If the difference you see is not within tolerances, then you cannot use that approach and must select something different.
You are not allowed to say "I'll follow the chart" or "I'll follow the box." They either match (by what I've described above) or they don't. And if they don't, you'll be flying a different approach or going to another airport.