This is often repeated wisdom, and it is quite wrong.
If the liquidity event involves the public stock market in any way e.g. IPO, merger, acquisition with a nontrivial part of the proceeds paid in shares of a public company - then you are forced to execise on one hand, and have a lock-up period, usually 6 months, forced by the underwriters or SEC rule 144.
That is, there is a mandatory 6 months wait between the forced exercise and the effective liquidity event.
This applies to investors as well as employees, BTW: I was bitten by this as an investor -- a modest 5X return on investment after 2 years turned out to be less than 2.5X return (still nice), but the taxes were paid on the 5X numbers, and the end result net of taxes was therefore 1.1X -- and it would have been a loss if everything happened in the other half of the year (luckily, I was able to net the gains with the losses because the 6 month lockup was april-october; but had it been october-april, even that wouldn't have been possible).
In two other tax regimes I've operated in, you are only ever assessed taxes in the event you can take money into your pocket. The US system is ridiculously unfair in this sense.