A few things:
1) Taking down a video generally never "solves" anything -- it just forecloses your other options. (For example, if you had a copyright strike, then taking down the video removes your option to submit a counter-notice or attempt to get a retraction from the striker)
2) "Giving credit" is not sufficient to avoid copyright infringement. So I don't want you to think that you can just put a blurb in your description or whatever saying, "oh, all copyrights to XXX". That's NOT enough. However...
3) If you have permission from the original owner and that is NOT who the content ID match is from, you should be able to dispute the claim either by saying that you have permission from the original owner or that the content ID match is not the right material (if you are in fact using the original and NOT the remix).