It's normally the opposite. Public markets are a lot better at judging intrinsic value than a handful of VCs. Every single private company out there is either wildly over or under-valued, more so at earlier stages.
They don't have short sellers seeking out reasons to tank it like the public markets do.
This is why companies with lousy future outlooks will sell for a lower price than their assets - debts.
There is no intrinsic value that private companies can stick to. They just have the power of controlling sales so they take sellers out of the market until they get the price they want at a volume they are comfortable with.
Stripe isn’t “intrinsically” worth anything that anyone will agree on. To one person it would be the cash in the bank minus liabilities. To someone else it would be a hefty multiple on that because they believe in the business.
https://www.valueresearchonline.com/stories/23354/intrinsic-...
It leaves out things like “what might the IP be worth to someone else?” and “What could the company do with better management?”
To your point, it’s frequently less than what the company trades at. Sometimes the opposite is true, and the company trades for less than the cash value of its assets minus liabilities.