LRD, going back to the "far/bar" video: It was part of an essay on perception, but painfully relevant to this thread I think! I can't find it again, but it would be fairly easy to reproduce.
The video shows a man saying nothing but "bar" and "far" repeatedly. The soundtrack, however, is a loop of him saying "far". He never says "bar" but, even when you know this, you can't help hearing the B sound when his lips form it.
It fascinates me for two reasons: I'm interested in neuropsychology, and I have a very good ear for language. When I read the link about an Irish 'broad T', I got it immediately although I don't recall having heard it specifically. However ... The point about the perception video is that people hear what they expect to hear. All of you insisting you're right and know precisely how one sound differs from another, knowing how it's formed, are ... plain ... wrong. When you look at a person forming a B but sounding F, you will hear B.
This obviously reinforces what others have said about people hearing "T" or "D" when the Irish speaker says "Th". If the listener isn't used to hearing a squashed Th, they'll hear what it looks like. No tongue sticking out, correct? And it's a dental consonant, so it must be T or D.
So, basically, everyone's talking out of their very erudite arses 
Glad you got the teacher sorted out, bella! Hope it goes well for your DC ... or should that be "Thee Cee" 