Then again, "Motor oil's motor oil", right? 
Fer Gawds sake, don't go there!!!
IMO, a K75RT with 55K on it and an iconic 22l in back for $1800 that starts, idles and runs well from cold start to warm, has no ABS warning, goes through the gears and stops well is not a bad deal. Those are things that even a sales person should be able to confirm in about 15-20 minutes, let alone a mechanic, even if they are an airhead mechanic.
I know the splines are a crap shoot. They are on every deal unless the seller lets you pull the final drive. You gotta look at the rest of the bike and decide if it's worth taking a chance. At 55k miles and original paint in the condition shown in the photos, I would guess that the odds are in your favor for good splines.
The AMA and BMWMOA stickers tell me that somebody before you was a serious rider. I would guess that person took good care of the bike during their ownership. Depending on how long that was, even if a later owner didn't maintain the bike, the time and miles of neglect are less than the 55k shown.
Having said that, even the best machines will need some work after 28+ years. The worst problems seem to come from years of idleness as the fuel rots everything in the tank, electrical stuff corrodes, and rubber rots. Starter brushes, ignition switches, engine seals are all items you need to consider needing work even on well maintained bikes. The seat and paint seem to indicate some outdoor storage in the sun. That may be an additional bargaining point, but don't count on it. If the paint is Mystic Red, it may not actually be faded, that color photographs and displays funny.
The idleness issue is why I suggested checking when the bike was last registered and inspected. A recent registration and DMV inspection will give you some idea of if and how long the bike has sat idle. I know that NY state has the mileage written in the inspection sticker. If that is the case in Michigan, it might give you a little more information on the recent past history of the bike.
