You're right that private corps. don't have "public pps", but knowledge of their share price (if they issue shares to employees) isn't exactly a secret. My old employer was an ESOP, employee owned, and we had a profit sharing agreement where 9% of our salaries was given to us once a year, in either cash for our 401(k)'s, in company stock, or a mixture of both. To calculate how many shares we got, the company valuation was determined by external auditors once a year, so we knew exactly what the pps was, at least at that time. I don't recall warnings that "if you share this data with anyone you will get in big trouble" - impossible to suppress that info in a company with > 1000 employees scattered in multiple locations in the US, where every employee knew the share price - very different from real insider info, where only a few key execs may be privvy to it, and where control of the info is determined by SEC rules/regs, on top of any company rules.
In any case, you are correct that "the pps" doesn't determine BO value - when we got BO, the premium was frigging ENORMOUS - shocking, to be honest - because the buyer put a huge valuation on the employees (engineers) they were acquiring, the only reason they wanted us - that would never show up in an external audit looking at earnings, cash flow, physical assets, etc.