JasonE
PRS Fan Boy
You said your guitar was the exact one in the video. That guitar has pickups with the square bobbins, which 59/09 pickups didn't have until just recently. The ones in the pictures in this reply are definitely 59/09s. I stopped the video at 4:39 and it looks like a splice in the negative wire going to the battery. My 53/10 pickups in my P22 are covered.
Did you get a hang tag with the guitar? That should state what pickups came in it stock. I have a P22 Trem that came with uncovered 57/08 pickups with the square bobbins. These are not something PRS typically makes and sells or puts in their guitars. This particular guitar is also a custom color for the model. They do some one off things like this at times but it would be noted on the hang tag. Another way to find this out is to send the serial number to PRS customer service and ask them for the build specs on the guitar. The will send them to you so you will know what the guitar was built with originally.