Someone is going to have to come along and verify, but this is my understanding...
5.56 NATO and .223 Remington are dimensionally the same cartridge.
However, 5.56 rounds are loaded to a higher pressure than .223.
And, .223 rifles have a slightly tighter chamber to improve accuracy.
Thus, if you put a hot 5.56 round into a tight .223 chamber, you can cause a KA BOOM, even though they are dimensionally the same round.
The reverse is safe, since 5.56 chambers are a looser and .223 is not as high pressured. Like Geronimo45 said, if you get something in 5.56 you are safe no matter what you shoot in it. You only need to be concerned if you buy a .223 rifle.
Lastly, there is something called a .223 Wylde chamber. This attempts to split the difference by using a tighter chamber than 5.56, improving accuracy, but still loose enough to handle 5.56 without any problems.