Do you have some examples of what precisely you mean by "a ridiculously long time?" Are these examples of specific states or dynasties, or just from archaeological documentation of a city existing at a site? A lot of this may come down to how precisely you define a "civilization." For instance, look at modern Germany or France. You can trace the current German or French people and culture back a thousand years, but the nations have undergone numerous changes in government, territorial boundaries, etc. When an early Mesopotamian civilization is listed as lasting for a similar length of time, the source may be using similar broad strokes as saying, "the French culture has existed for over a thousand years."