I interpret it to mean that meat is allowable if the monk or nun haven’t seen, heard or even suspect that it comes from an animal that was killed specifically for to be cooked into a meal for him or her.
Maybe venerable @dhammanando or @Brahmali could give us some insight into what do the paracanonical commentaries say about this?
And I speculate further that the main reason for this boundary was that without it things could quickly and easily slip into the religious sacrifice spectrum.
For example, in some middle east religions and cultures we have special dates in which lambs are killed for religious reasons and, as a result, people are left with quite a lot of meat to cook. Hence, the sacrifice becomes as well an excuse for a meat feast!