Not necessarily true. I have a colleague who gained his EASA Class 1 medical at Gatwick prior to beginning CPL training. He then decided to train in the Republic of Ireland and as per the rules it was required that his medical be issued by the same state as his licence issuer, so the IAA. He approached the IAA asking if he could transfer his UK CAA issued EASA Class 1 to an IAA EASA Class 1. However the IAA declined and made him do another Class 1 Initial in Dublin. This was in 2012.