However if a passenger is re-booked on another carrier at their individual request, then the ticket is endorsed to the new carrier. This permits the new carrier to receive consideration for the transportation. This is quite distinct from the situation where the original airline sub contracts another airline to operate its own service.
If the ticket is endorsed to another carrier and you accept that endorsement, then your contract is with the new carrier who will accept responsiblity for you in accordance with their own conditions of carriage.
This may be another of those legal versus customer service arguments that come up all the time in the SLF section.
As far as I am concerned, as a passenger, I have paid the airline money to get me from A to B. My contract is with that airline. If the airline can not uphold its terms of the contract then it can, as you say, either refund me my money and pay me compensation or arrange for its contract to be upheld (ie get me from A to B).
If it decides to get me from A to B on a different airline then fine with me; it is upholding its contract with me by sub-contracting this part of the service to the different airline. I have, when this has happened to me, never been told that my acceptance of this means that I no longer have a contract with the airline and now have one with the new airline - instead I am told something alone the lines of: "we can get you on a flight with Air Other leaving at X:XX - is this OK with you?".
No they haven't wet leased the aeroplane from Air Other - but they have sub-contracted the service of getting me from A to B to that airline. If anything else goes wrong then I would naturally talk to the airline that my ticket is with to get it fixed.