This is not really a mystery.
There are three means of understanding the regulation. The first are the Federal Register preambles applicable to the regulation in question, at the time the final rule was released. The second are the FAA Chief Legal Counsel letters of interpretation, which are available online for review and research. The third is the regulation itself. In that order.
Most who ask these questions haven't bothered to read the regulation. Most of those that do read the regulation have never availed themself of the Chief Legal Counsel interpretations, and fewer still have bothered to read the Federal Register preambles.
Ample material is available on this subject, in detail, most of it as answers to questions, with references.
So far as answering one's phone while in rest, the FAA has held that to a point, a single phone call from the company does not interrupt rest, nor require resetting the rest period. Should the company prove to be an interruption or provide ongoing interruptions, the rest cycle may be interrupted, and require starting again for legality.
No, you're not "always on rest," nor is there a universal truth that one is not obligated to pick up one's phone.
It pays to be familiar with the regulation. When the question of one's employment arises, if one is going to have a leg to stand on, one had better know which leg, and where it stands.