At the very least, a bank can look at stock in a private company, and before accepting it as collateral, demand to see cash flow and income statements, and perform its own valuations based on revenue, earnings (if they exist), debt to equity ratios, and things of that nature. With a token, pretty sure the analysis on that level becomes "so you just made these up?"
Now, whether or not this is how banks act in practice is another question. It is, perhaps, how they should act if they're being conservative, but it is likely that others will swoop in and often enough grab that interest for themselves. And in the rate environment we've been in until very recently, those are likely the banks that have managed to survive in many cases.
Also; stock in private companies is often not tradeable at all, but no accountant is going to call those fake.
There are multiple ways of plausibly pricing assets.
None are generally accepted that would let someone just make up a ridiculous valuation and stand up to any scrutiny, but people can always do what they want until the auditors show up anyway.