While I appreciate the sentiment OP, as the parent of a Y3 child who cannot read, I would be downright furious if those comments were made about my child, my parenting or about what was or wasn't happening in school.
While I appreciate you want to help, this isn't your place. I am aware of the issues surrounding lack of support/funding etc for SEND children, and the level of push often needed for the right support to be put in place (or indeed any support at all).
You say the family have a lot going on, so they're not advocating for their child, but you cannot possibly know this.
We must look like pure chaos to an outsider, we're late on a morning at least once a week due to school avoidance issues. I'm often 5 minutes late for pickup if my bus from work is cancelled and I need to get the next one. My daughter has explosive meltdowns, trying to communicate with her during these just escalates the situation. All people see is me often late, always with a child 'kicking off' with me doing nothing other than getting her from A to B.
What's actually happening is coordinated and consistent responses between myself and the school where we coregulate as best we can uo until she has to physically move between home and school, make the transition/transport as quick as possible to get her into a controlled environment where she can continue focused regulation activities. She has access to a sensory space and safe adults at home and school, she goes straight into those on arrival, and has as long as she needs there to regulate before a soft transition into class or until she chooses what she wants to do after school.
She had an EHCP, and the interventions/services involved run into double figures. I do not look like I am remotely in control of anything to an outsider. Most days I cry after dropping her off, because it goes against instinct to walk away from your crying child. Yet I am across absolutely everything. School do not share with other parents, and I have only shared with two other parents, only one from the school my children are at. There are a multitude of things going on in the background that nobody sees, and we're slowly making progress. Meltdowns outside of the travelling time to and from school are rare now. But it's the public ones that are yet to improve. To the outsider, I don't do anything, and things aren't improving. But that simply isn't the case.
I appreciate that you mean well, and I really don't mean this post to sound unpleasant, but acting like you can swoop in and fix everything with a bit of volunteer phonics after being in the vicinity of this child for one reading session is not okay, and likely not correct.