A "well actually" occurs when a person is splitting hairs. This can be desirable, for example when you're trying to obtain a complete understanding of something

A "well actually" occurs when a person is splitting hairs. This can be desirable, for example when you're trying to obtain a complete understanding of something. But in normal conversation, such pedanticism is often annoying. The "well actually" policy, as I understand it, is an attempt to make such hair splitting "opt-in" rather than "opt-out".