Sometimes the definition includes "type" or some kind of characterstic..
For example Barred Rocks. They're not considered rare by anybody. HOWEVER.. one "type" of barred rock from the show stocks from the very early days of the poultry show fancy IS rare or extinct by now. It's the type that has birds grow unusually crisp and clear barring and not the same(and supposedly even better than) as modern show barring type. It may seem not that big of a deal, it does represent a possibly valuable or just simply very interesting/"could have been valuable to today's show stock" sampling of specific genes that's rare or gone by now.
I've heard some comments regarding "most Delawares do not match the breed standard". They might have the color and pattern of a Delaware but perhaps most do not grow to very heavy sizes and lay very large eggs(if that is in fact the original Delaware standard was).
Another example to use are Marans. A common compliant is while a bird may look "Marans", they lay too light eggs. Are they Marans or not, if they otherwise match the standard in every way, except they lay light colored eggs? Some would say yes, others scream NO, must regularly a #4 egg or darker or it's simply not a Marans, no matter what.
It could be that the common Delaware is analog to a Marans that lays light tan eggs.. they may look like it but their traits or ?? do not match up to the supposed standard..
Not saying that's the case here with Delawares but I understand that is the reason some seemingly common breeds sometimes are included on various "rare breed" lists.
Or other times, an individual may be exaggerating, either intentionally or unintentionally.