Google gave me the exact same offer last year (assuming OP got offered 400 shares vested over 4 years, they were worth less at the time), and I have a very similar background. So it seems credible to me. The fact that I already had a lot of notionally valuable stock from a unicorn startup already vesting seemed to help a lot in negotiations. Then Google's offer helped me negotiate with everyone else (though I mostly applied to a different set of companies).
It was astonishing that people doubted the veracity of these #'s the last time this was posted a few days ago.
For how long is it considered ok to sit on an offer?