As with anything like this, there is very little in the way of what is right and wrong; only what is appropriate, and appropriate is subjective to the school and its own unique circumstances. That could be appropriate to education, to the school, to the child etc.
On the point of law, policy isn't law, it's only a term and condition. Twitter and Facebook are being used for some really good things in schools these days (both primary and secondary), most notably as said above like a broadcast account where the school doesn't follow any account, but parents and students can follow the school (once checked and approved).
In e-safety there is always 4 angles that must be considered - policy, liability, safe use, technology. If you think using the analogy of the fire triangle, i.e. if you have fuel, oxygen and heat you have a fire - so it is the same with e-safety, in other words if you have covered the school policy, the liability to the school (through misuse), empowered safe use, and using the right technology with the correct considerations, so you e-safety compliant.
In the case of using Twitter:
Policy - the school must have a social media policy (either separate or embedded within AUP) which states the controls for use.
Liability - the school must consider the implications of misuse by the school, i.e. risk assessment and mitigate.
Safe use - the school must empower ALL staff with good e-safety awareness, and include the students and parents
Technology - (using Twitter as the example) - a dedicated school account, locked, used as a broadcast account only (in the context of this post), users can only follow once accepted.
For the sake of being concise, that's a really quick description, but of course there are so many variables. As long as any school remembers the 4 principles and gives them due consideration any risk is mitigated.