It didn't say embarrassment increases support skills. It said the more serious the character is the more embarrassed they can get.
The explanation for her being a good fit for "dancer" was that a dancer's support skills uses the vitality stat (which she has a lot of) instead of spirit (which is her worst stat).
Ok, here's a direct quote from the manga:
This is yet another reason why I insisted that Natalia should be a dancer — embarrassment coefficient. For some reason, the more serious a character is, the higher this stat tends to be. Depending on the character, it can grant a boost to support skills. And in Natalia's case, that coefficient is an astounding number! 1.5 times the normal value!
—pages 41–42
As stated, embarrassment coefficient can grant a boost to support skills, and in Natalia's case that coefficient is 1.5 times the normal value. The fact that he mentions that it was part of the reason for him choosing this class for Natalia means that Natalia IS a character that benefits from this mechanic. So, yes, It did say embarrassment increases support skills.
Apart from that, it feels like nitpicking. Sure, instead of "
embarrassment increases the power of support skills," it may be "
embarrassment coefficient increases the power of support skills." That doesn't change much, does it? The whole points still is that the power increases because she's embarrassed, it's just represented in the form of a stat. Why do you think that was said while showing off Natalia being embarrassed in her new, revealing outfit?