Yes I see what you are talking about but to me, this is normal for your ISO/light condition. If you see the hair, you do see how much detail you already have for the light condition. Skin texture can definitely receive a boost from post processing Noise Reduction.
To reduce noise, you can use either a dedicated software such as NeatImage
(LINK to a free small size image download) or Topaz or many other softwares but as I suppose you already have LR to process RAW, you can use the noise reduction right there.
In camera post processing is not something I look for and more over you do RAW imaging to have Negative equivalent, that is no post processing at all, including No WB.
Is it fake to do post processing? Well if you do it carelessly or cook the image too much but in moderation, you can achieve a lot in a subtle way that is beneficial to image and pleasing to viewer's eyes. Harry (Who happens to shoot with your exact same camera) gave you a good sample of ISO 16000 with right exposure (And if I am not wrong, post process NR) to see how much can be improved so give it a try and see what you can achieve.