I'm afraid this is yet another case of the Guardian having a go at academies for being just like LA-controlled schools.
Mossbourne is an old academy and is therefore bound by its funding agreement. Under the Academies Act 2010 new academies have the same obligations as state schools with regards to SEN children. Indeed, most of the old academies (including Mossbourne) also have the same obligations as state schools under their funding agreements but there were some that do not.
LA-controlled schools can (and do) object to being named on statements on the grounds that admitting the child will have a negative impact on the education of other children already at the school. That is one of the grounds under which an LA can refuse to name the school nominated by the parents. Having advised a number of parents where the LA has refused to name the nominated school I can say that it happens far too often.
The real problem in both these cases seems to be that the LA caved in to the schools' objections - something that happens with LA-controlled schools as well, although I suspect that some LAs think (wrongly) that they are in a weaker position to force the issue with an academy. The LAs concerned should have forced the issue, in which case the academies could have appealed against the decision to name them instead of leaving the parents having to pursue the matter.
Note that the parents in both cases are taking action against the LA, not the academies. That is absolutely right. The problem is the refusal of the LA to name the school.