During play-testing my game, I'm continually having the same problem, and am seeing some of the testers experience the same Issue.
I've left the global setting so that any on screen text spoken by the character can be skipped (apart from cut-scenes). I find this works for a less frustrating user experience, when you can read faster than the game thinks you can.
The problem that crops up regularly though, is when a player clicks to skip a piece of on-screen text, just as the next line appears. This means they end up accidentally skipping the next line completely, sometimes missing a vital clue or story element.
As a suggestion, could the engine ignore text skip clicks for the first second or so of a line of text being on screen? (in effect you can't skip text until after 1 second)
This would give time for the players eye to notice the change in text, and solve the accidental skip problem. If this was toggle-able in the editor, it would still allow for developers to quickly click through text for testing.
I can appreciate this might mean a fundamental change to the way text engine works, but it can be a fundamental problem in story telling and puzzle solutions too.
Would be interested to hear other peoples thoughts/experiences of this.