It's not so much "it's right", but "it's canonical". FD presumably wrote the scripts for the Codex, including pronunciation guides for any technobabble which the narrator wouldn't have known how to pronounce. FD presumably also had several people listen to the Codex entry, before it went live in-game. None of those people in FD decided to "correct" the narrator or ask for it to be re-recorded with the "correct" pronunciation. And, especially in the article about the lady herself, it's kind of a big deal to "get it right" since, as it is a public database, theoretically, the Lady herself could obtain a copy and hear it too.
FD can of course change the canon at any time, by re-recording the Codex entry with a different pronunciation (they'd have to also redo a few of the other Codex entries where Aisling's name is spoken in the same fashion). But it's "officially and consistently in the game that way" for now, so we have to accept it as the current canon.
It's just like the spelling of the Imperial capital star system. In ED, it's spelled "Achenar", even though Wikipedia and every single real-world starmap and astronomy text I've seen spells it "Achernar". Even as I typed that last sentence, Firefox's auto-spellchecker is underlining the first, but accepting the second. But, since it's spelled "Achenar" consistently throughout ED (and spelled the same way int he prequel games too, I might add), we must deem it that that is the "correct" or "canonical" spelling for this star system in the ED universe, and will remain so until and unless somebody "corrects" this "error". Given the long history, it's probably too late to make this correction now.
For a second example, citing FD's capacity to change the canon: consider the name of one of the starports built out on the Colonia Road. It was originally named "Gigarin Gate". Some people assumed it was supposed to have been named after Yuri Gagarin, and called FD out on the mis-spelling. But meanwhile, since it was "Gigarin" in-game, "Gigarin" had to be considered canonical. I had head-canon that since a "rin" is one-thousandth of a yen, it must have cost some Japanese dude a million yen (a billion rin, or one gigarin) to build the base. Then a few updates later, FD unilaterally renamed it to "Gagarin". Turns out "those people " were correct in their assumption about the homage to the cosmonaut. So now, "Gagarin" is canonical and "Gigarin" is now non-canonical, a mistake which was corrected.
