—the committee can proceed to some things on unanimous consent, but it is a freedom with limitations. You cannot overturn the Standing Orders, for example, and you cannot overturn higher procedural authorities.
In this particular case, once you had moved your point of order and gotten the attention of the chair, and the chair gave you the floor legitimately, then you could seek unanimous consent. In the House, unanimous consent is really used to move along procedure, such as unanimous consent being sought for concurrence in committee reports of PROC, or for membership changes, for example. Those are the real reasons unanimous consent is generally used. In committee it can be used the same way. In this case, I would suggest that it was, but it did not pass.