all of my friends at google say the grant is in dollars and stays in dollars at google. at the end of the quarter you get a variable number of shares based on current stock price. While this reduces upside, it also reduces downside.
Your offer states that you will get $X of shares, vesting over 4 years. The $X is converted to a number of shares shortly after joining, based on market price, and is locked in from that point forward.
Your friends are mistaken.
I believe they used to due quarterly vesting for folks who didn't get much equity, but now that you can have vesting of fractional shares, ~everybody should be on a monthly vesting schedule.
This is a bit of a change from e.x. when I was hired and my offer letter said N shares, and so when I joined 6 months later my grant had increased in value significantly. But it's still not the situation in these other companies, where you vest 6.25% of the dollar value each quarter, converted to shares or whatever.
Actually that wouldn't really be compatible with googles vesting schedule, now that I think about it.