Can you call it "your data" if it is not being stored on your hard drive?
Much like how if I leave my phone in a taxi, either deliberately or accidentally, I don't own the taxi, but I do still own the phone.
If you create a replica of a taxi you rode in, you own that copy.
If you take a photo of someone, you own that photo.
If you write that person's birthday down on a piece of paper, you don't own their birthday now. You own the piece of paper with their birthday written on it, and they have no claim to that paper or what's written on it.
Opening a bank account using those details is identity theft, because they are not /your/ details. No one cares if you owned the paper you wrote them down on.
These are colloquially interpreted as "you have rights to your data". Naturally, your address is not generally copyrightable (another notion of ownership of data) but it can be "personal data" that relates to you.
Comparison: The bank's hard drives hold my money, but it's still mine and not theirs.