Frankie Rizzoli could not have become a cop the way he described. The Boston police, like all the cities and towns in Massachusetts, is Civil Service and requires that one takes a competitive exam and be placed on a list ranked by one's score. It is only after one is appointed to fill a position on the police force that one is sent to an academy. One can not just "go" to a police academy in this state.
Rizzol and Korsak would not have been able to sneak up on Brenner who was about to shoot Isles.