The channel partner has a key, and in theory he could cooperate with the sender of the funding transaction. So what I meant was that the sender could send the money to the multisig address using another funding transaction which competes with the "legit" transaction which uses your input. We would arrive then at the same problem you described: the txid would have changed, invalidating the commitment transactions.

However, I don't know if this attack makes any sense - could the channel partner access these funds or could they only be mobilized again if both channel partners cooperate and provide their signatures to close the channel?

Thantks for the link about dual funding - I will have to read a bit more about SIG_ALL and ANYONECANPAY so I can understand what you meant with the malleability attack vector.