I recently heard someone say that you don't have to use the internet to send a transaction in the BTC network. That the medium doesn't matter. That you could theoretically use SMS or a handwritten note, as two examples. I imagine they meant you could use any medium to communicate to a miner what your transaction is?
bitcoin network is working with the internet, the nodes all connect to each other via the internet, the miners then connect to these nodes. so you have to eventually have your transaction broadcast over the internet to these nodes.
the idea is that you don't have to personally connect to the internet and send it to the nodes, you could use an intermediary to do that for you. for example you could broadcast it using radio waves to send your transaction to a satellite[1] and that satellite broadcasts it over the network on your behalf.
i haven't seen other methods be used but theoretically it is true, you could use SMS,... to transmit a tx.
- other user already explained why giving private key is not needed.
[1]
https://blockstream.com/satellite/