16 bits (over 65 thousand discrete levels) of precision
Resolution != precision. It may provide 16 bits of resolution, that does not mean it will provide accuracy matching that. The datasheet shows a ±3mV total error at full scale input (2048 mV @860 sps), though lower sample rates should improve that, it's not 'over 65 thousand discrete levels of precision' in my opinion.
Let us rather say "Accuracy != precision". The device isn't much good if it doesn't return the same output level, for a given input level, each time. The mapping between output and input may not be correct (accuracy) but it should be consistent and there should be a consistent difference between , say, output level 32,500 and 32,501 (precision). If you want to argue that the device isn't really a "16 bit" ADC due to that ±3mV total error I can agree with that, ... but then why is it advertised as such?
Sorry, this may be a language issue, in my mind a precision component or instrument meant something that's both accurate at the start and repeatable (low drift and noise). Even if accuracy != precision I don't think that without looking at the noise and other errors, we can just assume an ADC to provide meaningful resolution to the LSB. I don't argue that it's not a 16bit ADC, because it is, I'm just saying that the OP shouldn't rely on it to be as accurate as it's resolution, which is a common mistake at first glance.
Yup, as long as you can repeat, integral non-linearity often doesn't matter if you're going to do a whole-system calibration... It's not like adc counts mean anything in real life anyway; you need to translate adc counts to real-life units at some point.
I think it's a bit daunting task, even with proper equipment, to calibrate a 16bit system. I think it's easier to start with quality components for which the response curves and errors are stated by the manufacturer and provide sufficent accuracy out of the box.