yes, the only way to be truly anonymous is pay and be paid with cash in exchange for BTC personally by hands.
Is it though? In order to make such a meeting you need to use a phone, text messages, a public place. Basically with every step of finding and successfully meeting with a person face to face you lose at least some part of the "anonymity" if not all.
You are quite right, unless you use it the anonymous tool such as encrypted ( REAL ) P2P you are free to revel to anyone what you are doing.
I mean bypassing exchanges you can be truly anonymous.