All they would have had to have done is drive along following the dog with their emergency beacons on until they got someone there that could deal with the dog properly or the dog got off the carriage way of it's own accord. They could even have tasered it rather than run it over.
Unless they dog has some understanding of traffic flow directions and lane discipline, I'm not sure how that'd help. It could easily run into the opposite carriageway, turn around and run back towards oncoming traffic, or leave the road entirely only to come back on five minutes later and cause an incident.
Use of Taser on dogs has mixed results, sometimes it can subdue them, sometimes it just makes them angrier and even less predictable. That's assuming officers at the scene were even equipped with Taser, and were able to get close enough to deploy it safely.
Theory: Dog was distressed. Dog bit police officer. Officer gets mad. Officer runs dog over in retaliation. Officer used red tape to cover up actions.
Reality: Police officers are human beings just like anyone else, exhausted other available practical options and sought advise from supervising officers/control room before resolving the situation. RPU cars also have video cameras which would have almost definitely been reviewed following the incident given that it's a use of a force.