The fire truck received the go ahead. They weigh 3x more than a normal firetruck. They're rushing to a different emergency. The plane is moving fast as hell. They can't just react instantaneously.
The ATC worker is clearly too stretched and such an incident was an inevitability. When they're shouting stop, they are no longer directly talking to the firetruck, which obscures the situation for everyone.
It is a terrible tragedy that will only be prevented with reform in staffing and safety procedures.