I am not familiar with the log and the cert to which you refer so cannot comment on those.
The odometer definitely has 6 digits so that sounds fishy. If someone tinkered with that, it makes you wonder what else they did to the car. 167k miles is about what you would expect on a car of this age. One of my '97s has 150k and the other has 250k. Both are great cars, but they have had a LOT of rubber and plastic parts replaced. Both have had their entire cooling systems replaced at least once (radiator, water pump, all hoses, etc).
I think that any 328 came with LSD, but I am not certain. My '97s both have it, and even my '04 325 wagon has it. With ASC, it does not really matter if you have LSD unless you intend to thrash the car with the ASC turned off.