When I listen to the Beatles' "LET IT BE", I can distinctly hear that the first T is pronounced like Polish or Russian or Spanish "R", only more quickly and softer. But when I watch "The Negative Reaction" episode from COLUMBO TV series, I can distinctly hear that when Lorna says "Mrs Peterson", her "T" is pronounced like Polish or Russian or Spanish "D", not "R". I asked my Tennessee friend about it and he says that he hears no differences. But I hear the differences! Even that edition of Advanced Oxford dictionary that I own says that "it is like a brief /d/ or the r-sound...". That is the dictionary implies that there can be two versions of flap-t. But all Canadian and American students I ask about it say that they see no difference. Can native British English-speakers tell me if I am right when saying that I see the differences in pronouncing this FLAP T.
For example, Abba pronounces "D" in "waiting" at https://www.youtube.com/watch?v=fZ7C127Q-GY. But they pronounce Polish/Russian "R" in "takes it all" at https://www.youtube.com/watch?v=iyIOl-s7JTU