First paragraph is correct.

The caveat would be that the capital gain during sale is calculated based on the difference from the price at vesting. So the original taxation is carried with you while you hold the stock which is the mechanism that you thought didn't exist for a reason.

For the second paragraph, it's not so different from real estate market fluctuations. You pay taxes based on the value of your property at a specific date even if that value tanks the very next day.