Erm sort of.
There is sightreading as a skill for an exam - you do a test where they give you a piece of music and you have to play it as accurately as possible first time, start to finish, with the right notes, rhythm and dynamics. Some people never get this skills.
Then there is playing through a more difficult piece that you will be working on 'at sight'. Some people try to cram everything in. Some work out the notes and approximate the rhythm and dynamics, some get the rhythm.... This is the actual skill of reading music and producing something from it but the first time you do it you are, by definition, sight-reading.
It's the same skill - the difference is in the relative complexity of the piece and the result anticipated.
The first teacher had an excellent approach IMO and your DD would benefit from that purely in terms of aural training and general musicianship from doing that at home. And the teacher is entirely right that scanning the piece before playing helps identify repeating patterns and the structure of the piece. Some start slow and simple but get v complicated (the page looks black!) but if you haven't looked through you go galloping off, run into difficulties and have to slow down so the piece sounds nothing like it should because the contrast in rhythm isn't there.
Basically when people refer to sight-reading they often think of the exam version, where you play it perfectly first time, and not the actual seeing-it-for-the-first-time sight reading and therefore have slightly unrealistic expectations of how good a first play through should be.
Does that make more sense?