Being a minor league union brainiac, I can see why you'd think so  

A pilot is assigned a base by the company from which the 50 mile radius is based.   He lives relative to that assigned base.   Then, the company assigns the pilot to work at another location, 45 miles away from his assigned base, but just inside the 50 mile radius.   He lives 35 miles from his assigned base in the opposite direction.

The company has assigned the pilot to ground transport himself 80 miles here from his residence (45 miles from his starting point).  Since miles doesn't equate to a specific time, the commute can be quite some time, which is a driving assignment directed by the company (thus, he is working as directed by the company).  

The FAA has consistently interpreted "rest" as a continuous period of time during which the
crewmember is free from all restraint by the certificate holder, including the freedom from
work and freedom from responsibility to work should the occasion arise. Legal
Interpretation to James Baxter, from Donald P. Byrne, Assistant Chief Counsel (Mar. 25,
1997). Duty means actual work for an air carrier, or the present responsibility for work
should the occasion arise.  See Legal Intepretation to Mr Boyle, from Rebecca MacPherson, Assistant Chief Council (Oct 12, 2012)

FAR 135.263(c) states: Time spent in transportation, not local in character, that a certificate holder requires of a flight crewmember and provides to transport the crewmember to an airport at which he is to serve on a flight as a crewmember, or from an airport at which he was relieved from duty to return to his home station, is not considered part of a rest period.

Local in Character is defined by the FAA as being transportation that is reasonably brief, that would be from a hotel or motel to the airport and back, or a pilot going to or from his residence to his primary base.   Going from your assigned base to another is not transportation local in nature, it is a ground deadhead!   It is duty, and not part of the rest period!  

CBA:

Regional Relief Pilots: Pilots who do not hold a regular work schedule and fill vacancies at any
base as directed by the Company in their particular assigned region.

Regional Relief Pilots shall have an ACCRA rating based upon an average of the bases within
the assigned region.

For the purposes of travel and mileage calculations for the Regional Relief Pilot(s), the
Company shall determine a primary location within the region as the start point. Travel within
50 miles (100 miles round trip) of that primary location start point shall be considered local in
nature, will not require an overnight stay and the Regional Relief Pilot shall not be eligible for
compensation, per diem or mileage reimbursement. When a Regional Relief Pilot is required to
travel the day before or the day after his assignment or more than 50 miles one-way from the
primary location start point of his assigned region to his shift assignment the Pilot shall be
compensated at time and one half for actual hours spent in travel and is eligible for per diem or
mileage reimbursement, if applicable.