We've got a couple options to explain that: like ourselves, K may be split between her mind and another, connecting through another packet. She may also be getting physical as well as mental assistance from K1 via her MUVI/Motor Control Chip.
Or, there may be another, additional technology (or CMC may do this naturally) that perhaps translates wants to words - letting her 'speak' without necessarily needing to think out sentences.
I find the most interesting option being that she's constantly in sync with the King - which is why she communicates with him so much. Perhaps it's true of all officers - Rooks, Bishops, and Knights. We're the exception because we're directly connected through the King's system - he can't be in there twice. Only, if that were true, all Consortium body scans would show that doublebrain that Keiran found.
Something interesting to think about.
There is a way to ask her about it (bring it up during the Kiril conversation and then again later, I believe immediately after the Queen conversation) but I didn't take that path for so long I don't remember what she says. It's very missable and tempting to choose a different option.
I vaguely recall her saying it's something all Knights can do. The problem with the remote control idea is that both the CMC voice and physical voices both are in her character. I don't think K-1 has the capability to duplicate that so well...
Yeah...I don't know...
Which begs the question - why does King sound like he's run through a voice synthesizer? Is it on purpose, to capture that he's not -really- the voices he utilizes?
If you try to spill the beans to Pawn 1, Pawn 1 says you sound exactly like the Consortium King.
The motor control means Henry can manipulate the muscles of the subject; therefore, everything said should sound like the individual saying it. Combining the above with that fact, I think we need to take "like" literally. It must have sounded like a very good Consortium King impression to Pawn 1 and Knight 15.
Going further, we know that Jasper and Moira are giving King voice on December 21, 2042. From that, we can guess that Bishop 6 mimicked Jasper whom is about the same age (22) as Bishop 6.
King's voice is synthesized most likely because of the uncanny valley effect (the more human-like something is, the more repulsive it becomes to humans). I suspect the sound Bishop 6 produced would sound like the synthesized Jasper we hear later in the game. If it weren't synthesized, I think it's safe to assume they wouldn't jump to the conclusion it was King's voice.
I said "character" for a reason. The sound of the voice in meat space and through CMC should sound identical to Knight 15, controlled or not. It's the "character" of it that I'm not sure King can reproduce. That is to say, Knight 15, in both of the conversations, says things that fit Knight 15's character.