There's a reason why such moments are called "ideal". That's because they're idealized, not real. They are a simplification of reality.
One way you could get an ideal moment in a beam is by welding two rigid vertical bars at the midpoint, one above and one below the bar. And then apply opposing forces at the extremities of the bars. As far as the beam is concerned, it will suffer an ideal bending moment, without any associated forces:
For something a bit more reasonable, imagine the following structure. Beam C is the only one with any loading (ignore self-weight). It is supported by beams B, which are themselves supported by beams A, which are supported by pinned supports at their extremities:
The fixity at the connection of beams B and C means that beam C will suffer a (small but non-zero) bending moment at the connection, which gets transferred to beam B as a concentrated torsional moment (along with the shear support reactions). Likewise, the connection between beams A and B will have the same bending moment in B transferred as torsion to A. However, the torsion in B also gets transferred to A as a concentrated bending moment.
Obviously, these concentrated bending-moment/torsion transformations can be easily described in terms of internal force couples as well.