WWI combatives ,from my reading was started by a Captain O'Brien and a Captain Smith,both Jujitsu Black Belts trained in Japan.
These men were directed to start a H2H training program as Jujitsu was seen as an answer to trench warfare.
These men beagn to teach their skills on a limited level in 1917-1918.
The Army though believed that their system,which was in place prior to these men's activities were better and the Jujitsu did not go very far.
(some have said this WWI film was made for propaganda purposes to instill fear in the enemy)
WWII comes around and men like Captain Smith were still involved in teaching Jujitsu to the military,then we had Biddle and the USMC,and others who saw a need for something more during the end of WWI and had been training to use a jujitsu,boxing,wrestling mix.
The most influential use of Jujitsu based materials was acquired and taught by Fairbairn.
It was seen as a more concise program,easy to teach,easy to learn and effective for close in H2H.
Fairbairn's methods,along with others along the way to include men mentioned at the start of this,was taught to Britsh and American Rangers and Commando types,it was taught to the OSS and SOE,and portions filtered into US Military H2H across the board,US Army,USMC,US Navy and each branch had men who created systems of usage which became variations of WWII Combatives.(With Fairbairn's being the easiest to implement)
We had Fairbairn,Sykes,O'Neil,Styers,Biddle,Smith,Wesley Brown and many others.
So while men like Captain's O'Brien and Smith had a hand in the start of jujitsu implementation in the US Army in WWI,it did not take off until WWII and the best proponent was by far Fairbairn's development.
Just my view from my readings on these men and these arts.
I am sure others with more research can add more.