This is entirely surmise and may have no basis in fact, but is it possible that when the P 38 was designed there were still some patents in effect covering Browning design features that Colt and/or FN owned?
Also the P38 was designed to be an easier and cheaper pistol to manufacture than the Luger(the pistol it replaced), is it possible that it also was cheaper and easier to produce than Browning designs?
Could also be a case of: we don't want a foreign designed gun for our German military.
And last thought, maybe it turned out that the P38/P1/M92 dropping block system, for whatever reason it was developed, turned out to be just as good as the Browning system. Remember most pistola today using the Browning tilt barrel system have gone to the Sig lock-up system (Sig, HK, Glock, Ruger, Walther, some S&W and the new Russian service pistol).