Google's description of how Chrome sync works has the following warning:
Don't sign in to Chrome if you're using a public or untrusted computer. When you set up Chrome with your Google Account, a copy of your data is stored on the computer you're using and can be accessed by other people using the same computer. To remove your data, delete the user you are signed in as.
If you take Google at their word, this indicates that signing out still leaves the synced information stored locally.
Of course, you can use Chrome without ever signing in, but as soon as you do, you have no control over what is spread around through the sync function. As I said, I use Android devices and I also have ported my home and business phone numbers to Google Voice to keep them when I dumped the landlines they were attached to. This means I need to sign into my Google accounts regularly. I just don't use Chrome to do so, because I don't want whatever is cached locally from other sessions to be synced to those Google accounts.
You're entitled to your own opinion, but not your own facts. You don't have to assume anything. Significantly more detailed information about how Google Sync works is available on Google's website and the settings themselves make it more than clear. The first time you sign into your Google account using Chrome the settings are chosen by Google, meaning sync everything. If you've already signed in and unselected any of the options, those items will not be synced to the next computer you use.
Google's warning is absolutely true for most people because the settings are hidden and once you've logged in there are no obvious warnings about that. That's dishonest and wrong (some would go so far as to say evil) but still completely different than what you're claiming - by your own admission based almost entirely on assumptions.
No, people shouldn't sign into Chrome because Google refuses to take security or user choice seriously. If you have to rely on FUD to justify it you're not paying enough attention.
