Not necessarily. My husband’s company that I was referring to was publicly traded, although much smaller than Google or Facebook. They took care of payroll taxes due on the value of the vested stock; we paid the income tax to the IRS quarterly. The value of the stock was included in his W2, however if we waited until we filed our taxes we would have incurred penalties, on top of a hefty tax bill.
Companies like Google may handle things differently, and companies that deal in RSUs may as well. My point still stands that you need to understand the tax implications of your offer.