I'm sure those home visits would be videoed the LA would want to cover their arses as well with people like the Minghams. Sarah38 would make all sorts of bullshit up as they did with "Mr Wonderful" our man PaulOhh I stop reading the thread for a couple of days and something happens! I haven’t caught up but will do this afternoon!
With regards to the visit, they can refuse it. Basically the LA ask for information about your provision, you respond(usually in the form of a report), they will either be satisfied or not satisfied. If they are statisified you would usually expect annual contact If not satisfied they need to advise you of their specific concerns so that you can address them, so they might say they have concerns about the provision you have for maths and you can go back to them and clarify what provisions you make, maybe adding more detail. If they still aren’t satfified then they can start with a SAO(school attendance order) which goes through court to get the children back into school.
Some people do choose to have visits but as a rule it is advised to keep contact in writing rather than having visits because of some LA’s majorly overstepping the mark. Some children find it very frightening and overwhelming having visits particularly those with SEN. Keeping things in writing means you have evidence of everything that both sides have said and done.