...and other synced data.
If you purge your local sensitive data in one of computers (i.e. on shared PC) while you're logged-in to your Google account then -- due to some serious stupidity in Google Chrome -- you will purge the same set of data from your Google account as well. Each device that syncs data with this account will, as a result, purge its local sensitive data next time it contacts Google servers.
This article presents a list of solutions you can try to apply in situations like this.