You made a great job of "Across the Borderline", Dan. You may feel more comfortable now having removed it but there probably was no need. It is such a well known song that I am sure if there had been a problem it would have been recognised immediately and they would have just stuck an advert on it. There are lots of covers of that on youTube and not everyone (if anyone) will have asked permission. The adverts actually bring more income to the copyright holders so I am sure that some of them like people doing covers of their songs, permission or no permission :).

You and I do not make any money from our YouTube channels; we just do it for fun so maybe when YouTube wishes to point something out to us they could do it politely.