Herzfeld paid the initial bills. Herzfeld said "ARPANET was not started to create a Command and Control System that would survive a nuclear attack".
Lukasik came in later, and had no signing authority or supervisory position on the initial ARPANET work.
Following your guideline, the ARPANET therefore wasn't "created to have a war-proof network for army use"; that was a design goal which came later, after the collaboration goal.
Yes, but in the end it's he who pays the bills who decides. Without them it's lights out.