I don't think the law implies that at all. There is no obligation to travel the same speed as a vehicle, except when riding two abreast. A cyclist traveling slower than the vehicles still obtains full right of a lane. A rider can't take up an inside lane unless passing or making a left hand movement.
(a) Except as provided by Subsection (b), a person operating a bicycle on a roadway who is moving slower than the other traffic on the roadway shall ride as near as practicable to the right curb or edge of the roadway, unless:
(1) the person is passing another vehicle moving in the same direction;
(2) the person is preparing to turn left at an intersection or onto a private road or driveway;
(3) a condition on or of the roadway, including a fixed or moving object, parked or moving vehicle, pedestrian, animal, or surface hazard prevents the person from safely riding next to the right curb or edge of the roadway; or
(4) the person is operating a bicycle in an outside lane that is:
(A) less than 14 feet in width and does not have a designated bicycle lane adjacent to that lane; or
(B) too narrow for a bicycle and a motor vehicle to safely travel side by side.