  We show that failure of local realism can be revealed to observers for whom
only extremely coarse-grained measurements are available. In our instances,
Bell's inequality is violated even up to the maximum limit while both the local
measurements and the initial local states under scrutiny approach the classical
limit. Furthermore, we can observe failure of local realism when an inequality
enforced by non-local realistic theories is satisfied. This suggests that
locality alone may be violated while realism cannot be excluded for specific
observables and states. Small-scale experimental demonstration of our examples
may be possible in the foreseeable future.
