Don't cloud the issue - your either in rest or out of rest.
When your in rest, you have no obligation to the company...phone, pager, horn, etc.
Companies are allowed one contact during a rest period without considering it an interuption. Answer, don't answer - it's up to you.
Regardless of what your company assigns (hotel duty, airport standby, flight asignment, etc.) it can't be considered rest.
You have to have 10 hrs, uninterupted rest within a 24 hr period.
Yes, the company can shorten or lengthen any rest period, as long as the above criteria is met. Obviously, 2-way communication is required to do either. Hence, the original question...Do I have to answer the phone?
Answer it, don't answer it - it's up to you.
That about sums it up...well said.