I am not sure how you have "never seen a reference to" the FBI having issued the Colt Police Positive, as it is readily available on the internet and in the NRA magazine American Rifleman (August 2011 issue).
Please note that the FBI's first issue handgun was the Colt Police Positive, not the Official Police. The June 28, 1933 report of the weapons committee notes that the Police Positive was already supplied to each field office, and should be issued to each agent. The report can be found here:
http://historicalgmen.squarespace.com/storage/33GunCommittee.pdf
The condition placed on adopting the .38 Special caliber was that the .38/44 ammo be adopted. The .38/44 ammo was the forerunner to the .357 Magnum, which was not yet introduced in 1933. The .38/44 ammo was VERY HOT by today's standards, and fired the 158 grain Keith semi-wadcutter bullet at 1125 feet per second, which is a low end Magnum round. The round was a Smith & Wesson project, to be fired in its big N-Frame revolvers, known as the .38/44 Heavy Duty (fixed sight) and the Outdoorsman (adjustable sight). Naturally, the little Police Positive must have been a joy to shoot with that ammo! The ammo report is found here:
http://historicalgmen.squarespace.com/storage/3845comparison.pdf
The initial order for Police Positive revolvers so that the Bureau would have enough so that one could be issued to each agent is found here:
http://historicalgmen.squarespace.com/storage/33colttraining.pdf
The directive to train each agent and the distribution of Police Positive revolvers by field office is found here:
http://historicalgmen.squarespace.com/storage/33ordersdistribution.pdf
As you can plainly see, the Police Positive was the first issue revolver for the Bureau. In case you missed it, the official publication of the National Rifle Association (NRA) had an article on FBI handguns, and it also said the Bureau issued the Police Positive revolver. The article can be found here:
Guns of the FBI History
I hope you enjoy reading all of these original memorandums as much as I did. We certainly owe a debt to Larry Wack, (FBI Special Agent, ret.) for obtaining all of these historical documents and putting them on his site so we can all see them.