The bonding of the neutrals should have provided a clear fault path, but keep in mind they were not designed to handle the primary system. I would think the higher voltage would provide even better fault clearing current than the secondary voltage for which they were designed (unless it just burnt them open).
Evidently the system was weak or was never intended to handle this type fault. I would expect it to be able to handle a transient delivered to it. This transient was located at the secondary system, not just delivered through its connection to the primary through the transformer.
Even so, "touching" the ungrounded conductor to part of the MGN should not be a better connection than a connector made for the purpose of bonding the primary and secondary neutrals together.
The neutral bond to the MGN should have been the main path for current. The protection scheme for the primary would normally consider a high-impedance ground fault. This estimated impedance might be on the order of at least 40 ohms to a 100 ohms or so. This minimum fault design criteria should certainly have been more than the impedance seen by the bonded neutrals in parallel with the 4 rods (the 4 rods being the smaller contributer to higher fault current).
Finally, it could just be that the primary system protection was not adequately designed to handle minimum faults or that the "weld" was a high impedance connection. What did the analysis show?