When you send a transaction, you provide a cryptographic signature to the network. It’s mathematical proof backing up the fact that you have the right to spend it.
It’s semantics but that’s what I’m getting at.
Discussion
I agree, we're arguing semantics here. "Backing" has the historical context of hard assets being represented by paper notes. Maybe with the adoption of Bitcoin, people can have a better way of understanding what makes Bitcoin work, what backs up it's value, because of it's open source nature. It's easier to inspect what holds up Bitcoin's value than gold's, for example.