Why would the giant, hungry, blood-crazed basilisk obey Tom Riddle or Ginny under his influence, or really anybody, and not simply go out and eat on its own?
Basilisks are controllable by Parselmouths
The creation of Basilisks has been illegal since medieval times, although the practice is easily concealed by simply removing the chicken egg from beneath the toad when the Department for the Regulation and Control of Magical Creatures comes to call. However, since Basilisks are uncontrollable except by Parselmouths, they are as dangerous to most Dark wizards as to anybody else, and there have been no recorded sightings of Basilisks in Britain for at least four hundred years.
Fantastic Beast and Where to Find Them (2001 textbook) - Basilisk
It would appear that snakes must listen to what is told to them in Parselmouth. For instance, at the Dueling Club:
Harry wasn't sure what made him do it. He wasn't even aware of deciding to do it. All he knew was that his legs were carrying him forward as though he was on casters and that he had shouted stupidly at the snake, "Leave him alone!" And miraculously — inexplicably — the snake slumped to the floor.
Harry Potter and the Chamber of Secrets, Chapter 11
And when Tom Riddle tells the Basilisk to attack Harry, he's ordering the snake, and the evidence that we have is that snakes must obey a Parselmouth's orders.