The circuits all over the place on this one but I don't see these facts fitting according to the strictest rule.
It is within the discretion of the police to decide whether delaying
the arrest of the suspect will help ensnare co-conspirators, as
exemplified by this case, will give the police greater understanding
of the nature of the criminal enterprise, or merely will allow the
suspect enough "rope to hang himself."
U.S. V. Garcia 79 F.3d 74 (7th Cir. 1996)
See also Hoffa v. United States 385 U.S. 293 (1966)
A suspect has no constitutional right to be arrested when the police
have probable cause.
The police are not required to guess, at their peril, the precise
moment at which they have probable cause to arrest a suspect, risking
a violation of the Fourth Amendment if they act too soon, and a
violation of the Sixth Amendment if they wait too long. Law
enforcement officers are under no constitutional duty to call a halt
to a criminal investigation the moment they have the minimum evidence
to establish probable cause, a quantum of evidence which may fall far
short of the amount necessary to support a criminal conviction.
EDITING THE ANSWER in light of some comments.
Florida recognizes sentence manipulation and outrageous government conduct as defenses. United States v. Ciszkowski, 492 F.3d 1264, 1270 (11th Cir. 2007) Outrageous government conduct and sentencing factor manipulation focus on the government's behavior. Outrageous government conduct occurs when law enforcement obtains a conviction for conduct beyond the defendant's predisposition by employing methods that fail to comport with due process guarantees. Under this standard, the conduct must be so outrageous that it is fundamentally unfair. See United States v. Ofshe, 817 F.2d 1508, 1516 (11th Cir.1987)
In the Ciszkowski case, the defendant was charged with murder for hire as part of a sting. As part of the sting, the government provided Ciszkowski with the gun. The gun had a silencer, the silencer converted his crime to a more serious offense. Ciszkowski argued that he did not know the gun had a silencer and accused the government of sentence manipulation. He lost. The court tells us that the standard for establishing that the government's conduct is sufficiently reprehensible to constitute sentencing factor manipulation is high as gives us some cases where the court declined the finding.
See United States v. Bohannon, 476 F.3d 1246, 1252 (11th Cir.2007 (government's selection of age of "minor" victim for sting operation was not manipulation even though the selected age resulted in enhancement under guideline);
United States v. Williams, 456 F.3d 1353, 1370-71 (11th Cir.2006) government's purchase of crack cocaine rather than powder cocaine was not manipulation despite sentencing differential);
United States v. Sanchez, 138 F.3d 1410, 1412-13 (11th Cir.1998) (government informant's selection of a fictitious amount of drugs to be stolen by defendants was not manipulation of the quantity)
Now, about this doctor. The reason this is might be troubling is that this doctor might have entrapped the suspect. For example, if the suspect went to the dr and just wanted some aspirin but the dr convinced him to ask for vicodin and pain killers in some excessive amount (I don't know, I do not want to make up facts). This could be entrapment by a citizen acting purely on his own; if this is the case there is no entrapment. See Worley v. State, 848 So. 2d 491 (Fla. Dist. Ct. App. 2003)
However, when the person making the inducement is acting as an agent of the government, courts may allow an entrapment defense. The government is responsible for the actions of its agents. But keep in mind that you still need to establish both elements of entrapment.
Per United States v. Isnadin, No. 12-13474 (Feb. 12, 2014):
The entrapment defense involves two separate elements : (1) Government
inducement of the crime, and (2) lack of predisposition on the part of
the defendant. The defendant bears an initial burden of production to
show that the first element, Government inducement, is met. Once the
defendant makes this initial showing, the burden shifts to the
Government to prove beyond a reasonable doubt that the defendant was
predisposed to commit the crime.
For any of these defenses to work, the guy who was filling the prescription can not have been predisposed to commit the crime except for the actions of the government and its agents inducing him.