I should probably post it in the lore section, but It is game specific.
It's Khajiit. But yes, Khajiit can learn to speak in 1st person. You shouldn't look at games for 100% lore correctness, Bethesda is known to break their own lore or change it on the fly if they're lazy or don't have time to create things as they should be by their lore.
I noticed it with Tsavi. It's actually dialogue specific to her that isn't shared with Argonians.
I always just assumed she was more well-spoken because she was raised in Cyrodiil or something and so she's more attuned to Cyrodiilic-style speaking instead of Ta'agra. She is part of the Leyawiin court, after all.
Actually, it seems to be true of a lot of Khajiit in Leyawiin. Even Shomara, the "dumb-as-a-post" sister of the Three Sisters Inn speaks in first person.