Since neither of us were there, we can only take G's transcript at face value.
My assessment was based on the events around G's timing point 4:35, in which it is established that G-HIM has misheard/misunderstood the traffic position ahead of him. The FISO correctly acts to re-state the true position of the traffic, but then does nothing when the transmission is not acknoweldged by G-HIM. 25 seconds elapse before the incident, during which time the FISO will (one assumes) have observed the aircraft getting closer than one would hope and yet says nothing.
Whilst a FISO cannot instruct an aircraft in the air, more information could conceivably have been passed to avoid the risk that the situation gave rise to. The FISO could have been more pro-active in ensuring that G-HIM really did appreciate the position of other traffic in the circuit.
Once again though, we were not there, and I am basing these comments purely on what G has been good enough to share with us.