I noticed you answered your question yourself after having written the answer, so here it is anyway (TL;DR: you are right).
A technical question:
Is it possible to receive a BTC amount on-chain from another person and simultaneously open a LN channel for him/her for me with the same transaction, if the sender cooperates?
Yes, but only if the sender effectively cooperates as otherwise your funds would be stuck in limbo.
You need to:
- Start the funding process with your peer (here you get the keys to form the 2of2 Script)
- Get the sender to create a transaction which pays to this Script and hand you the txid
- Complete the funding process with your peer by exchanging the commitment transactions refering to the txid
- Have the sender broadcast the transaction (hence trusting them to not change the transaction, which would change the txid before doing so.
FWIW, it's possible with c-lightning if you want to try this out with the (dangerous) fundchannel_start, fundchannel_complete commands.
Or even better: use a BTC amount on-chain transaction and refund an already opened channel (this would be a kind of splice-in)?
It's possible in theory but has not been spec'ed. You can find some discussions about this on the #lightning-dev ML (end of 2018 iirc).
I imagine this could be useful if exchanges offered this service. You could withdraw an amount on-chain, and instead to have to do the channel opening transaction yourself additionally, the withdraw amount is added to an existing payment channel or opens another one to a LN node.
Yes, splice-in / splice-out would be great (and a lot of people are looking forward to it) but is quite complex state-machine-wise.