No, this is a wrong argument. We can specify arbitrarily low temperatures by hypothesis, obviating the objection. If you want to get pedantic you could note tha

No, this is a wrong argument. We can specify arbitrarily low temperatures by hypothesis, obviating the objection. If you want to get pedantic you could note that measuring something that is, say, 10^-30m is unphysical - not even laser interferometry gets that small, or anywhere close. However, given that the argument uses a counter-factual, you'd have to extrapolate all the ways that would affect apparatuses. Instead, my way is simpler by generating an absurd result that if you could build and measure a thing to arbitrary precision you can encode infinite information into it. This is enough for me to reject the counter-factual without going through the messiness of thinking through hypothetical realistic experiments. The one interesting place to consider is at the Schwarzchild radius of a black hole, where presumably information accumulates to an absurd degree, monotonically over time. I don't really know enough about it to comment intelligently, so I won't except to note its existence.