No, if you undo the screws on either side of the bracket, you can rotate the camera the other direction. One drawback is you won't be able to use the markings on the side of the bracket to line up the camera because the camera will be in a different position. I was able to eyeball the angle and it worked fine though.
First time poster, got some great tips here on how to mount the trailer camera so I figured I'd post pics of my install in case it helps others.
I have a 26' Travel Trailer so the cable length and hookups were perfect for my setup. Instead of drilling holes for the camera mount, I attached it to the camper with 3M super strength vehicle molding tape. I also placed the camera bracket upside down to avoid having the loop of cable out the top of the camera. I painted the cable white to try and blend it in a bit to the color of the camper. I also bought an extra Camco battery box to hold all of the slack cable at the front of the camper - I just drilled a couple holes on either side of the box to run the cable through. I used Cool J's tip to run the cable underneath through 1/2" non-metallic Liquidtight Flexible Conduit through some of the camper frame cutouts and I attached it in a couple spots with a some Line Clamps.
Took it on a trip over the holiday weekend and it all worked great - love having the rear view transparent trailer option.