Looking at a film-chronology and drawing "this one copied that one," "this one stole from that one" conclusions is overgeneralizing and misleading.
Army skits like the drill routine were a staple of vaudeville and burlesque comedy performers for decades. It was standard practice "in the business" for performers to borrow from one another, with all types of routines. The best performers, like the Stooges, could take the old routines and give them their own spin thru their own talent and personalities.
SALT WATER DAFFY was produced for Jack Haley, and with Vitaphone based in Brooklyn where it used NYC-based performers to cast its films, and considering Haley's fame on vaudeville and Broadway stages, it's quite possible that Haley himself had stage experience with the old bit, so Henley & Lambert constructed an appropriate script.
BUCK PRIVATES was not inspired by BOOBS IN ARMS. Abbott & Costello had their
own version of the drill routine which they had been doing in burlesque since they teamed in 1936, and notably on Broadway in 1939 in THE STREETS OF PARIS. And it takes a lot more than one 2-reel short to incent a competing studio to finance a feature film. Universal had a new comedy team who were nationally popular on radio, U.S. involvement in the European war was inevitable, and the U.S. re-instituted the draft in the Fall of 1940. Real life events had more to do with BUCK PRIVATES than anything else, and similiar projects were underway at Fox for Laurel & Hardy (GREAT GUNS), and at Paramount for Bob Hope & Eddie Bracken (CAUGHT IN THE DRAFT).
Joe Besser starred in the nationally touring YOU'RE IN THE ARMY stage revue in 1937 and 1938. The drill routine he did in HEY, ROOKIE! (1944) and AIM, FIRE, SCOOT (1952) was adapted from that stage show; the bit was also frequently performed by him on
TV variety shows from 1946 thru the 1950s, e.g., HOUR GLASS (5/9/46), THE KEN MURRAY SHOW (10/14/50) and Spike Jones' CLUB OASIS (3/29/58).
Jules White visited Besser during an L.A. run of YOU'RE IN THE ARMY in late September 1937. A month-and-a-half later in November 1937, the Stooges are filming WEE WEE MONSIEUR (1938), with a drilling scene that borrowed liberally from both Besser's and A&C's acts. Coincidence, inspiration, or "copying"? BOOBS IN ARMS (1940) did the same a couple years later, and much more blatantly from Besser.