If I'm wrong about all this, then I look forward to a comprehensive refutation

If I criticize projects mentioned by you it won't look good.
Check what these projects say about themselves. Start from the project 1 -
http://lightning.network/lightning-network-paper-DRAFT-0.5.pdf. For example, read section 5.5 and tell me how nanopayments are possible.
5.5. Fees
Lightning Network Fees, which differ from blockchain fees, are paid directly between
participants within the channel. The fees pay for the time-value of money for consuming the
channel for a determined maximum period of time, and for counterparty risk of noncommunication.