I use react inline styles in some situations where it's appropriate. on large tables or SVG (eg. with zillions of styled circles) there will be issues.
if you are sending HTML from a server with inline-styles then you will have much bigger problems with bandwidth.
This is where tachyon and basscss can provide a clean way for the day to day simple styling tasks like "needs more padding here" "make that title bigger there" without writing up stylesheets with repetitive margin, float, etc. for every single view in your app or every page on your website.
I assume he/she means that CSS is cached as an http resource and can be reused in different pages, whereas style attributes are only cached as part of the page; ie using them adds page weight.
Practical example: I have a form with a header. I look at it and think "there needs to be more space below the header". So I change
to It hot-reloads etc. It took me exactly two keystrokes to change this and I know that the spacing is consistent with all the other spacing in my app.