Okay, I'll play.
1) Not true. Not anymore anyway. It used to be true. But nowadays, it is impossible to say that the average law-enforcement officer is of less-than average intelligence, because the average high-school gradudate goes on to get some college, whereas the average person does not. Since there are very few law-enforcement officers who have yet to graduate high school, and since most of them have GED's coupled with at least SOME college education, who therefore qualify for the same par as the average high-school graduate, it is only a very very small percentage of law-enforcement officers who can't be argued as having above average intelligence.
But that does not mean that they aren't idiots nor that they aren't stupid, just that they might not actually be exercising the intelligence given to them that they could.
2) Between being picked on as a kid and the TV shows showing who it is that gest to get away with paying them back by beating them up or killing them, is what initially attracted me to the idea of becoming a police officer.
One badge-bearing bully I had the displeasure of meeting, became an officer because he had become his school's bully and wanted to continue bullying people after he graduated, but it was not that he was picked on as a kid and then became a bully after becoming an adult.
The policeman who deputized me on two occasions had also been bullied as a kid, and had taught my whole Boy Scout troop how to use his firearms, recognizing them as a part of his job, but, unlike your rumor, would choose to step into situations he got called into much like the Mayberry flavor of TV cops, without his sidearm, without adequate backup (once it was JUST me, which is why he deputized me) and with so little fighting skills that I could best him at wrestling when I was still in Jr. High School. So, I would have to say that his purpose for getting into Law Enforcement had nothing to do with a desire to bully anybody back, just to be there to prevent as much bullying as he figured he could.
3) Since at least the turn of the previous century, I have not heard of anybody who had only been to school for eight weeks before being given a badge.
This particular rumor might have something to do with your state's minimum-lenght academy.
Police academies used to be a substitute for high school, much like normal schools or nursing schools used to be a substitute for high school.
Nowadays, however, you can't even get accepted into a police academy without at least a GED, which is the equivalent of graduating from High School with a D-minus grade-point average, so at least a lot of high-school education is required.
College, however, is not.
So, it is true that after proving someone has the wherewithall to gradueate from high-school, it can only take an eight-week cadet program for someone to meet the minimum requirements in your neck of the woods.
But, not in one of the states where I have lived.
In that state, there ARE no academies.
In that sate, it is a requirement that you be compelled to attend school from the fall after you turn five years of age until the day you become sixteen, but beyond that, there is no statute-required minimum education to become a gun-toting, cruiser-driving, badge-bearer.
On job sites, education levels are posted by individual law-enforcement agencies, as a means of discouraging the lesser-educated from applying, but, when not enough of the more-educated apply, they have to lower their standards, and guess what... they wind up hiring someone who didn't know how to read well enough to know that people of their lack of education weren't supposed to have submitted an application.
In that same state, it has been proven that you don't even have to be able to read the instructions that come packaged in a box of bean-bag shot-gun rounds in order to start shooting them (and wind up, thereby, killing someone in the process).
The standard SHOULD be a whole lot higher, but it isn't, because the majority of the people in that state think that since badge-bearing bullyings only happen to a very deserving minority, it isn't until they find themselves in that particular minority that they even BEGIN to believe that things are good enough along that direction as they need to be.
Me, I would actually WELCOME a rumor such as this one of yours to be true in that state.
For that reason (among many) I recommend avoiding Oregon when and if you can.