It's very true to say that clipping should never be allowed to happen in a digital recording. A 16-bit recording has 65,536 different possible levels and you are allowed to go up to level number 65,536. But you can't go to level 65,537 because there isn't one.
During recording, your equipment, whether hardware or software, should be able to tell you whether you have attempted to go 'one above', but if you missed the warning, or ignored it, then the recording you make will not store this information. There will be no clip light showing when the recording is played back.
This is because the recording can only store valid levels. The fact that you clipped the input isn't stored. The level will go up to 65,536, then stay there for the full duration that the clipping occurred.
And of course, the signal might just naturally have alighted on 65,536 for several samples in a row. It's possible, and not necessarily a clip.
So, if a clip cannot be detected on playback, is there some way it can be inferred? Of course, you'll be able to hear it, but it would be nice to have some objective confirmation.
The answer is that it is highly unlikely that any real-world signal would produce more than one or two consecutive full level samples. For there to be three 65,536's in a row would be an extreme situation. Four or more and there is something fishy going on.
So in equipment that does appear to indicate 'overs' on playback, you can be sure that this is not an accurate indication that clipping occurred. On the other hand, because it is counting consecutive maximum levels, then when it counts four or more it's pretty sure that you naffed up.
So, clipping during recording is defined as when the signal level goes higher than the maximum that can be encoded. On playback, it is usually held to be when there are four or more consecutive maximum levels.