The claim that the general army ant ecological strategy only evolved once is not necessarily hyperbole. (I don't have enough information or background knowledge to evaluate it.) But the "exactly the same" business... Yes, that is hyperbole, for the reasons I've stated.
Mutations are the exception, and a favorable mutation would be even more of an exception. If a species is doing well in its environment, we would expect it to persevere, relatively unchanged. An *isolated* mutant variety could eventually develop into a new species, but the parent stock could continue to exist unless something comes along that wipes it out.
Over time, as a result of occasional isolated mutant populations, there can be a great variety of closely-related species. The mosquito, for example, is said to have 3,000 different species. Perhaps one of them is still the same as the original. This is not a problem for evolution.