I've always had a problem with some of the songs that are used to remember what an interval sounds like. Particularly, the ones whose melodies don't start on the tonic. For example, Here Comes The Bride is used for a perfect fourth interval, but that interval is not 1 to 4. It's 5 to 1. Similarly, My Bonnie Lies Over The Ocean is used for the major sixth. However, that's not a 1 to 6 interval. It's a 5 to 3. So as accessible as these songs are, I feel like they've not giving good tools to hear notes relative to the tonal center of a given piece of music.
I trained my own ear by learning to sing the major scale in my head and then counting the degrees until I just knew which was which. So, having to sit through classes that didn't teach it this way made these other exercises seem like a hindrance. Can anyone confirm or deny my suspicions about these songs? And are there alternatives to learn melodic intervals relative to the root?