A guess, as I can't say what was in Reg's mind. Bodhran is a word essentially popularized by Sean O Riada in the 1950s. Before that, the instrument existed in various places in Ireland, sometimes as a ceremonial drum for wrenboys and so forth, sometimes as a winnowing-pan. It was called by different names in different places, and my guess is that Donaghue's family, who after all had been playing music long before O Riada popularized the term Bodhran, called it a tambourine themselves.   

You can go back to the 1920s, and find records of Irish music with Bodhran on them, and it was generally called a tambourine then by recording musicians. Reg knows this well, as that era's music is one of his areas of expertise.