Is it correct, based on Sheikh Al-Albani's statement that the caller is the one who initiates the greeting, to not start with "peace" when answering the phone, even if this causes surprise among friends?

It is Sunnah for the caller to begin with salaam, as he is in the position of one knocking on a door. The person being called should respond to him. It is forbidden for the caller to remain silent after lifting the receiver until the person being called speaks, as this goes against the Sunnah and because the caller is the one making the request.