Because there is an actual manuscript difference between the Masoretic Hebrew and the Septuagint Greek.
Both translators were pretty faithful to their source, but the sources differed.
So the question is whether there was corruption in the Hebrew or the Greek. On the one hand, presumably the Greek, itself being a translation, contained errors that must be perpetuated if we use it as a source. It's worth noting that this was Brenton's own opinion in the introduction:
... the unequal character of the version: some books show that the translators were by no means competent to the task, while others, on the contrary, exhibit on the whole a careful translation
the defects found in the Septuagint—its inadequate renderings, its departures from the sense of the Hebrew, its doctrinal deficiencies
On the other hand, most of our extant Hebrew manuscripts are much more recent than our Greek ones, and skeptics of faithful transmission across centuries will point to this as a reason to suppose the Septuagint's sources are more authoritative.
We might prefer to use internal evidence, of course, or archaeological evidence. I know nothing about the latter, but as to the former I can note that while the negation is pretty easy to understand — the next few verses have several "they took X, but not Y" that the Septuagint translators might have mixed up — there's no clear source for "Azotus", which doesn't sound like any of the Hebrew words. Hence either they interpolated or they had a Hebrew manuscript that differed from ours.
A bit of wild speculation would be that the text was revised as the territory changed hands, since such accounts are often assumed to retroactively explain the author's landscape, but that's also an archaeological question far beyond me. :)