For some reason now unknown, Colt spelled the word "calibre" on all its auto pistols in the pre-WWII era. The exact number of Model 1903 pocket hammer pistols made is unknown due to confusion with Colt's serial numbering and the numbering of the later guns in the same series as the Model 1902 pistols. Those guns are not really rare, but are uncommon in good shape and one in 100% could bring upwards of $4000. Of course, here we have only the seller's word for the condition, and ones in top original condition are really rare. (Mine is a nicely done reblue, but a reblue nevertheless.)
The Model 1903 pocket hammer pistol (not to be confused with the .32 Model 1903 pocket hammerless) is a dual link pistol, like the 1900 and 1902 models and the later 1905 model in .45 ACP. It is chambered for the .38 ACP, with a case dimensionally the same as that of the .38 Super,* but less powerful. (Use of .38 Super in that gun could seriously damage the gun or injure the shooter.)
The "gangster" story sounds like hype - I know of no reason or evidence that that model was any more a favorite of the criminal element than any other gun of the time.
*In spite of gun markings, the .38 ACP/.38 Super and .32 ACP are not actually "rimless", being of the case type we call "semi-rimmed."