I think this is an error. (And so are "significant figures" as commonly used.) 2.4 +- 2 and 2.0 +- 2 are quite different estimates even though you wouldn't (according to conventional wisdom) be justified in giving more than one "significant figure" for either. Using the number of digits you quote to indicate how accurately you think you know the figure as well as to say what the number is is a hack. It's a convenient hack sometimes, but that's all it is. Everyone knows not to round intermediate results even when starting with low-precision numbers. Well, your final result might be used by someone else as an intermediate result in some bigger calculation. The same goes for probabilities. It is very important to know when your estimate of a probability is very inaccurate -- but that's no reason to refuse to estimate an actual probability. Even if you just pulled it out of your arse: doing that makes it a very unreliable probability estimate but it's still a probability estimate.

That assumes that someone isn't calibrated. If someone calibrates his intuition via frequent usage of prediction book and by always thinking in terms of probability he might be able to make precise claims without following a precise method. If someone would claim "1.21% chance of FAI" success by 2100 I would agree with you that the person didn't learn the lesson about significant figures from high school chemistry. I don't the that issue with someone claiming 1% chance. If you want to get calibrated it's also useful to start putting numbers on a lot of likelihoods that you think about, even if the precision is sometimes to high. It allows you to be wrong and that's good for learning.