Earlier quoted context omitted.
Gmail allows you to send from your other email addresses through the web interface. It is nice having multiple accounts in the same mailbox so they can share labels. I don't think it's a violation of trust to have mail forwarded from one account to another account on the same provider. Email does not have an implied amount of security or privacy. Sending email is like sending a postcard--Anyone involved in its transi…
Unless things have changed recently, sending as an address other than the Gmail account you're sending from results in a tacky "On Behalf Of" clause that displays both addresses to the recipient.
This leaves no evidence of your personal account, even in the headers.