Yes, in principle, absolutely. It wouldn't be practical though. The detectors are large, and sensitive to every kind of noise and interference, and you need to collect data, not just take a mere single reading. But, funny story, during commissioning the Chinese officials in charge of the nuclear plant were very conservative about what information they wanted to share with the experiment regarding the plant's operational status, I got to see them with some funny looks on their faces when the physicists told them, and showed them plots of exactly what was going on in the reactors and when.
Edit: Ok, let me not be so brief. In short, the current detectors for monitoring reactors are either HUGE (rooms and rooms full of highly purified water, and even those just look at nearby reactors and only get 1 count every 3 days). Or the detectors are very close to the reactor (7 meters i.e. https://www.iaea.org/safeguards/symposium/2010/Documents/Pap...). So signal to noise is the main issue first of all.
More like they're looking at fuzzy pictures of something that might be really really interesting, but isn't quite in focus enough to tell. Kind of like what you might come across in a crypto-zoological situation. They need a better picture to feel comfortable they aren't the boy crying "big foot".
I understand why that may be the case, but IMO your link was a prime example of science done -right-. The researchers saw something they couldn't explain, and even knowing that that they almost certainly made a mistake somewhere, they put their hubris aside and asked the community for help. This sort of discovery should be commended, not avoided!
Sure, the instrumentation problem was found eventually, but it would have been even better if it was found much earlier, before speculation bounced around the internet. There are quieter ways than a publication to get other eyes on the problem -- like a site visit by a review team.
The mainstream (and wannabe mainstream) media care about lurid headlines, and not much else (apart from the occasional agitprop piece, maybe). Even the most guarded of press releases are regularly distorted beyond recognition. Good luck with the media management!
