I'd get pretty damn frustrated too if I couldn't ever play in peace
I agree BOTH behaviours should be being addressed - while no one deserves to be 'bitten' if you are invading someones space and making them feel threatened you are increasing the odds you WILL be bitten and need to make better choices!
Children construct their own intelligence. The adult must provide activities and context, but most of all must be able to listen. Children need proof that adults believe in them. Their three great desires are to be listened to, to understand, and to demonstrate that they are exactly what we expect."