Let's us forget an instant about the chemical method and concentrate on whether the current method is accurate. And let's of course leave aside the non-interesting question whether one is accurate and the other even more accurate.
Consider these 4 possibilities involving these two factors: Are the CO2 levels increasing stably (A) and, are the current measuring method accurate. (B)
A = False
B = False
This is virtually impossible, it would mean that somehow, the fluctuating CO2 in reality, line-up to the erratic measurements to create a straight line increase. This is statistically impossible.
__________
A = True
B = False
Impossible, an inaccurate tool would not be measuring a stable increase like it does now.
__________
A = False
B = True
Impossible, an accurate tool would show that the CO2 levels aren't increasing stably. This is at odds with the image shown above.
__________
A = True
B = True
The only possibility that make sense. The current tools measure accurately.
It follows from this that if another method, which ever it is, does not confirm that levels are steadily increasing, that this method is in fact inaccurate for it's impossible to trump the fact that current method is measuring accurately.