NOT A TEACHER
I cannot give a definitive answer, but I have consulted several English dictionaries and none of them making this mention. Oddly enough, if you google "countermeasures against natural disasters" (note that it should be plural) you will see that a lot of the results link to Japanese websites .
Edit. A "measure" is defined by Longman as "an action, especially an official one, that is intended to deal with a particular problem." A natural disaster is not intended, so when you're dealing with a natural disaster, you're not really countering an intended action (and therefore it's not a countermeasure). That may be what your dictionary is getting at.
- For Teachers