"The gun will need X number of rounds through it befre[sic] it will function reliably."
This should read :"The gun will need X number of rounds through it before it is trusted to function reliably."
Obviously, if the pistol just shot 500 consecutive trouble free rounds, it
was reliable. Now....can it be reasonably predicted that the pistol will
remain reliable? Past performance is an indicator of future performance, but it is not an absolute predictor.
If your round count for carry is 500, 1000 or 50, after you shoot that amount, detail strip the pistol and inspect it dirty, looking for wear patterns. Gunpowder residue can tell you a lot if you let it. Then clean each part and inspect each part while cleaning, looking for cracks, etc. Finally, reassemble the pistol and shoot it some more, trying any way you can to get it to jam. Ride your thumb. Shoot it sideways. Upside down.
Even then, you can not 100% guarantee it will fire on the next trigger pull. The odds however, are in your favor. Remember, past performance is not an an absolute predictor of future performance. Machines fail unpredictably every day.
FWIW, many machines with very close tolerances are designed to have a break-in period, where metal parts polish each other to a final fit in a bath of oil rather than rouge. This technique of finely fitting machine parts has been used on internal combustion engines of all types, clockwork, and other devices. Some gun makers have borrowed the technique and now use it on closely fitted firearms, namely the 1911. The real question is whether that is a good thing. Does it improve accuracy? Does it improve reliability? Does it improve durability? Those are aspects that will be debated for years and years, as long as the 1911 remains popular.
The fact is, gunsmiths from Jim Clark Sr. to Ted Yost have improved the accuracy of the 1911 by tightening the gun. Some gunsmiths have compromised reliability in doing the same thing. Some 1911 manufacturers recommend this break-in period on their guns. Others do not.
Those are the facts. Draw your own conclusions from them.