We will have to disagree with the terminology being used.
Tracking inert gas IS decompression. Inaccurate stop depth time is not.
Yes. It is just terminology. I think "tracking inert gas" as a synonym for "decompression information" is completely wrong. But, I reckon it's just my opinion and you are entitled to your different one.
Your inert gas tissue loading is tracked. It's a factual mathematical model (in the sense that the numbers produced by the model are standalone facts, which may or may not match any actual physical properties).
Your decompression requirements are a completely different thing. The computer calculates them based on the tracked inert gas tissue load, what Gradient Factor settings you have chosen, what Last Stop Depth you have chosen, and depth, plus assumptions that the computer makes like what your ascent rate will be and what gases you will switch to during the ascent.
You can call inert gas and deco the same thing, but knowing my inert gas tissue load does not tell me what stops I'm going to make and for how long. The calculations based on some defined parameters and some assumptions is what tells me where to stop and for how long.
You say decompression information is a synonym for inert gas tissue loading. I regard decompression information as a synonym for my ascent plan. Certainly, if we were planning a dive together and I said "what is your plan for deco" I would expect you to tell me stops and times, not some description of your anticipated inert gas tissue loading.
In the end, the important fact is that if you set your computer to think you are carrying gases which you are not, then the inert gas tissue load it thinks you have will be correct (with regards to the model - but may not have any correlation to your actual physical tissues). But, the ascent plan it tells you will be wrong. It will self-correct as you ascend. But, when you are on the bottom and looking at your computer and it says "go up, stop at 20 for 2, stop at 10 for 10, and you can get out within the GF parameters you have set" that info is wrong.