That is not what the CBA says.   

Seems pretty cut and dry!   RAD is the approval authority for scheduling such training during your normally scheduled work periods!   Without his approval, it's not approved!   Nothing give the pilot the final decision, as you claim, nor the Training Department. 

C. The Training Department is responsible for scheduling training dates and locations. Pilots
shall attempt to schedule training during off-shift periods. Training scheduled during
periods when a pilot is normally scheduled to work at a base require approval by the
Regional Aviation Director. A Pilot participating in centralized training will be provided with
the ability to self-schedule during his early and base month up to one hundred and eighty
(180) calendar days prior and no later than sixty (60) days prior to the first day of his base
month and is encouraged to schedule this training during his off-shift period. If a Pilot fails
to self-schedule training prior to the sixty (60) day period that is prior to the first day of his
base month the Company will schedule the Pilot for mandatory training dates and times.
A Pilot participating in decentralized training will have such training scheduled at the
Company’s discretion based on aircraft or instructor availability.