as eldon points out, there is often a significant difference in the ammo. And anyone with the reamers can tell you that 223rem is not the same as 5.56.
however, the real source of confusion is that the gun mfg are guilty of marking their chambers wrong in a shockingly high number of cases, and even when they mark them correctly, their worn reamers and sloppy machining often mean undersized or oversized chambers.
Just my opinion, but most "223" barrels out there are not exactly 223Rem, but are actually using a reamer the mfg custom ordered with slightly different specs similar to the Wylde chamber. This change to the chamber makes it a little safer than a real 223 Rem. As a result, you get the sort of "well, everybody else does it so it must be safe" advice, which despite being mostly true, is still bad advice because somebody somewhere with a real 223Rem chamber and real 5.56 ammo could be at dangerously high pressure, and if you combine a few other environmentals, like ammo laying in the sun, a dirty chamber, etc and they could get hurt.
Better safe than sorry. Call the mfg if there is any doubt and ask. they will probably tell you it's totally safe.