Here's an example that I think garners more agreement that properties of a limit ("really understanding") don't necessarily mean that any path towards that limit has the properties of the limit. I think there's a lot of room for disagreement about whether this is a factually-accurate analogy and I'm not trying to argue either way on that, just trying to answer your question about how one might make these sorts of arguments if one has a certain belief about the facts.
Let's say we're trying to build a calculator that only needs to do integer addition. And we decide to build it by building a giant if-else chain that hardcodes the answer to each and every possible addition. And due to finite resources, we're going to hardcode all the additions of integers up to absolute value N, but we will increase N over time.
Everything you said applies equally to this situation: it quacks like a duck, and when we talk about things it can't do we have to continually move the goalposts each time a new version comes out. It also has the property that there is a "scaling law" that says that each time you double N you get predictably better performance from the system, and you can do this without bound and continually approach a limit where it can answer any question indistinguishably from something we might call "true understanding".
But I think it's a bit easier to agree that in this case that it's not "really doing" addition and is a bit short of our wish to have an artificial addition system. And if someone touts this system as the way to automate addition we might feel a bit irritated.
Again, many people will say that this is a bad analogy because LLMs operate quite differently, and I'm not trying to argue for or against that. Just trying to give my explanation for how a certain understanding of the facts can imply the kind of conclusion that you are trying to understand.