I am glad they admit you are "correct", though the waffle about separate entitlesd should be ignored as it is incorrect, but I am glad you got most of your money back however I believe your tickets cost £11.80 each so Southern owe you £3.60. I will assist in writing a letter requesting the balance if you like.
I would recommend anyone using a Southern only ticket on any service operated by Southern to not hand over any money. They will then have to issue an Unpaid Fare Notice, which I predict will be cancelled. I will assist in appealing the UPFN.
Is anyone else planning to travel on Southern only tickets on services operated by Southern? If so, please do get in touch for some advice to ensure you are prepared in case Southern decide that the service you are on will not be honoured. Also, be prepared for a similar battle when using an out-boundary Travelcard routed Southern only within the Zones on SWT.
My advice is always to be prepared, act calm, be polite, refuse to hand over any money, but co-operate with the UPFN, draft up a letter, ask me (and other fares advisors) to proof read the letter, and then send it to them. We will assist in any way we can when you use a TOC-specific ticket on TOCs you are entitled to use it on.