This might have been true at one point (I know it was) but my phone didn't have my Google account on it for a few days. I could use it, except I couldn't sync my contacts or presumably use the play store. It came on but not with any accounts attached.
Was this when you initially got the phone or did you set it up and delete the account later on? Last I tried you can set up the phone and use it with no Google account, but once you add one you can't remove it without resetting to factory defaults.
