They also used crude but informative observations during the period last year where they were still trying to find the right balance. For example at reactor 2 they had seen steam from containment entering the upper building levels. When they looked again later (perhaps September) after making various changes to water flow rates & location , they saw no steam and the paint had flaked off of the overhead crane, suggesting the atmosphere was now much less humid.
They shouldn't have used the term cold shutdown, since that implies a routine state and this situation is anything but, and the term 'relatively stable' is fairer in my book. Relative to how unstable the reactors were earlier on, newsworthy events in the reactors that can be detected by humans have been few since the early months.
Knowledge about the state of the cores is obviously far more limited than we'd like, but its not surprising that it will take years to learn more. In the meantime I don't think many would claim that the available monitoring data is perfect, especially at reactor 2 where there are far too few correctly functioning temperature monitoring devices working in many important parts of the reactor. Indeed when many of these sensors started to go wrong, resulting concerns about reactor 2 temperature rises were the biggest safety scare we've had for a long time, until they decided it was faulty sensors rather than actual temperature rises. I think they just lost another temperature sensor at reactor 2 the other day, although it may not yet have officially been declared as broken quite yet. So they better hope the mission to try fitting replacement sensors works, though its certainly not an easy mission and the state of the reactor core may well be responsible for the problems they have already faced with an 'obstruction' at the end of the pipe they originally wanted to use. In the meantime they will just have to rely on temperature indications in other parts of the reactor, and observations such as the steam one I mentioned earlier.