I think that whether you use the term sight-reading `correctly' or `incorrectly', both interpretations of `sight-reading' are improved by regular practice of prima-vista sight reading. I'm not convinced that you need always to practice prima-vista sight reading at performance speed -- unless you're really wanting to improve your skill as an accompanist. But I'm open to argument on that one. I try to practice both slowly with a view to getting decent accuracy, and fast with a view to getting to the end of the piece without screwing it up completely.
But I'm not a maestro, either. If you were to put a piece of piano music in front of me of, say, grade 3 ABRSM standard, I couldn't promise not to play a note wrong, even though I'd probably describe such a piece as `easy'. I'd probably play many
of the notes right, unless it's in a style I'm not familiar with. The closer it is to baroque, the greater the likelihood that I'll make an accurate job of it, just because I'm most familiar with music of that era, and there are certain correspondences between composers and pieces.
When I go wrong when sight-reading, what usually happens is not a failure of sight-reading as such -- it's not that I get to a note or a sign and think `What the heck's that?' Or play an E when it should be an F. Usually what happens is that I find I don't have a finger in the right place to get on the note. If I'm accompanying, I just skip the note. In fact, if I'm accompanying I sometimes skip more than a few notes