I suspect that some parents cannot distinguish the difference between what their child is capable of alone and with one to one attention/assistance!
Really? What exactly are your suspicions based on I wonder?
I recently posted on bornfree's own thread about home/school reading disparities. My DD finished reception on white, level 10 and is now on Topaz, level 13 and has been level by her teacher as working comfortably within NC level 3. Just like bornfree's DD she's just finished Matilda and is now re-reading Charlie and the Chocolate Factory.
The only reason this is possible is because in reception they assessed children using a benchmarking tool, all children were allowed to take at least one book home a night, sometimes more and usually 2 a weekend. They had incentives for the more reluctant reader (5 books read = a tiny prize).
What I am quite sure of is that if she went to a school where all the books in each level needed reading, then she wouldn't have reached level 13 by now. She needed the opportunity to achieve her potential, by allowing her to read often, not a rule that tries to keep as many children as possible at the same level.
I accept that some parents don't fully understand the difference between decoding skills v comprehension skills and may assume that because a DC can read their current level effortlessly then they should move up.
However, this pre-occupation with 'barking' at print that usually comes up on a thread like this really bugs me. Barking at print implies a lack of comprehension and I can't imagine that a child would do this for pleasure. I imagine a child would only bark at print if requested, like a performing seal. Therefore a child that chooses to read chapter books for pleasure must be understanding them to a greater rather than lesser degree. Further more a child can only read with expression if they understand what they are reading. If my DD is reading out loud I can tell if she doesn't understand a sentence fully because of how she reads it. I'm sure I'm not alone in being able to do this, despite 'only' being a mum.
A child that can 'perform' at a much higher level at home versus school is something that needs investigating to understand why, not just dismissing with the assumption that it's because the parent provides one to one attention, which, in any case, is very different from assistance.