For example, human eyeballs are really bad at it. Staring at a microwave that has been recklessly modified to run without door, or with a hole in the door, is most dangerous by turning the eye's inside which is similar to raw egg white into the cooked form: cooked egg white is unsuitable for a lens due to the very strong scattering from the coagulated proteins. I'm sure other temperature sensitive parts exist with poor cooling, as they're not naturally expected to be able to get dangerously hot without the surrounding tissue heating it.
The lack of thermal effects they mentioned where whole body temperature; while hard to actually measure, I'd suggest thinking of the temperature of the blood in the arterial venous heart half when it comes to potential overtemperature. Yes, if the body as a whole has cooling issues, this blood that is about to enter the lungs (after coming from all around the body) is going to be overly hot. But if the bottleneck is the lack of blood vessel density in e.g. the eyeball, this temperature issue won't show up when measuring in the heart.
The RF was probably too low power to produce readily measurable effects on temperature in the brain. I imagine that it could be a difficult piece of data to collect. However, you're undoubtedly correct that whole body temperature wouldn't be informative in such a study.
Makes sense, keeping some distance from running microwave ovens is a good policy. After an oven has been in service for some time what are the odds seals become leaky, etc. Probably not a great risk but no harm in minimizing one's exposure.
If the door mechanically seals properly like it's supposed to, all should be fine. If the mechanics make it not be as flush as it used to, get rid of it or measure the RF power at it's operating frequency near it while it's running, to check whether it still properly seals the RF.