Browning did indeed provide grip and manual safeties on his pocket hammerless pocket pistols - both at Colt and Fabrique Nantionale (FN). They were aimed toward civilian sales where firearms experience and training was unpredictable. He didn't consider that to be the case where his exposed hammer military pistols were concerned, perhaps being influenced by the old Colt Single Action Army model of '73, which was popular in frontier Utah where he lived.
So far as the military pistols are concerned, he had been retained by Colt for the specific purpose (among others) to develop a sidearm for the U.S. Army and hopefully other foreign military services, and he did just that. Throughout the process he would design a prototype. Colt would make them, and the Army would conduct trials. Browning personally attended all of these, and when necessary made adjustments or repairs on the prototypes as might be needed. All of the other companies involved sent hired "mechanics" to do such work. When the trial was over and reports of the results submitted, Browning would again go back to his drawing board, using both his own experience and the reports for guidance. Colt then, lost no time making whatever was called for. While there was sometimes some disagreements between Browning, Colt, and the Army concerning the best way to go, there was never what might be called an adversarial relationship, as the were all working toward the same goal.
So far as a dropped pistol discharging was concerned, Browning believed that his inertial firing pin design provided sufficient protection to prevent that. He might have been wrong, but at the time there wasn’t any evidence to suggest it.