If that’s the case, a clearer term might be “authorization”. “Right” is typically thought of in the legal sense.

You could say you’re only authorized to broadcast a valid transaction if you have bitcoin in your wallet. But even that’s a bit misleading - the network isn’t “authorizing users” so much as it is simply validating transactions.

Also, when you buy bitcoin, who is granting you this “authorization” to spend that bitcoin? Not the network, but the party you’re buying from.