I find your statement partially incorrect. I have "rebuilt" 2 bikes, including my current 2006 Hayabusa. A bike that has been down hard enough to destroy it, that really needs to read " A bike that has been down hard enough to destroy the plastics and tank."(or plastics and cluster) That will total a bike out. Plastics. What a joke. Come to think of it, all 3 of the bikes that I have owned were all salvage/rebuilt salvage.
I have never had any weird problems with them. People really seem to shy away from them, but in actuality if say a bike low sides, the flips and high sides and they claim it on insurance, it will be totaled more than likely. Even if it is a low speed accident. I purchased an 04 sv650 that was totaled for plasics, muffler and footpeg. All I did was buff plasics, replace footpeg and re connect cannister. Got it inspected and it was good to go!
In Ohio, the inspection process really just wants proof that you own the parts. Does not necessarily inspect for "safety." You have to provide receipts for the parts you purchased. If from a dealer, you only need the dealer receipt. If from a private party, you need a vin of source vehicle, seller name address phone i believe, and a notarized bill of sale. You can use ebay parts, just better to buy from a ebay seller that has an actual business. Because that way you just have to get a receipt from them as they are a business and not joe schmoe selling parts off his buddys friends bike..
I looked up Indiana laws briefly and it seems very alike Ohio law. Link here
Indiana Salvaged Vehicle Regulations and Consumer Protections - DMV Guide
So in short, No you can not buy a salvage bike and ride it how it is. You may be able to somewhat get away with it, by making the bike naked if lower fairings are ruined. Or by repairing cracked/rashed plastics yourself. You should call one of your salvage inspection branches and talk to the trooper and see what he can tell you. It all seems much scarier than it really is. Just make sure you dont start with a bike that is complete trash. There are lots of salvage bikes out there that are fairly easy fixes, with 95% cosmetic damage. As all of mine have been.